BasicMath.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "Basic Math"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "import math"
      ],
      "outputs": [],
      "execution_count": 1,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "1 + 1 # Addition"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 2,
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "metadata": {}
        }
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      "execution_count": 2,
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        "inputHidden": false
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    },
    {
      "cell_type": "code",
      "source": [
        "2 - 1 # Subtraction"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 3,
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 3,
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        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "8 - 9"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 4,
          "data": {
            "text/plain": [
              "-1"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 4,
      "metadata": {
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    },
    {
      "cell_type": "code",
      "source": [
        "2 * 8 # Multiplication"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 5,
          "data": {
            "text/plain": [
              "16"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 5,
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    },
    {
      "cell_type": "code",
      "source": [
        "8 / 4 # Division "
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 6,
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              "2.0"
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      ],
      "execution_count": 6,
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    },
    {
      "cell_type": "code",
      "source": [
        "20 // 6 # Division, removed devimal values"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 7,
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 7,
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    },
    {
      "cell_type": "code",
      "source": [
        "20 % 6 # Shows remainder for division"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 8,
          "data": {
            "text/plain": [
              "2"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 8,
      "metadata": {
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        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "3  ** 2 # ** means raised to the power"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 9,
          "data": {
            "text/plain": [
              "9"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 9,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "16 ** (1/2) # Squared root  "
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 10,
          "data": {
            "text/plain": [
              "4.0"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 10,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "8 ** (1/3) # Squared cube"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 11,
          "data": {
            "text/plain": [
              "2.0"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 11,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "abs(-8) # Absolute Value"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 12,
          "data": {
            "text/plain": [
              "8"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 12,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "7%3 # 7 mod 3 - modulo"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 13,
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 13,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# round decimal point to 2 places\n",
        "round(3.1468, 2)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 14,
          "data": {
            "text/plain": [
              "3.15"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 14,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Logarithmic of x to base b\n",
        "# log(x, b)\n",
        "math.log(64, 2)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 15,
          "data": {
            "text/plain": [
              "6.0"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 15,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "PEMDAS - Parentheses, Exponents, Multiply, Divide, Add, Subtract"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "3 + 3 * 3"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 16,
          "data": {
            "text/plain": [
              "12"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 16,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "(8 - 5) * 2"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 17,
          "data": {
            "text/plain": [
              "6"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 17,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "12 - 8 + 4 * 2 - (6 / 3)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 18,
          "data": {
            "text/plain": [
              "10.0"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 18,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Fractions"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "from fractions import Fraction\n",
        "# Fraction(numerator, denominator)\n",
        "\n",
        "d = (0.25, 0.5, 0.75, 1.25)\n",
        "for the_decimal in d:\n",
        "    print(Fraction(the_decimal))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1/4\n",
            "1/2\n",
            "3/4\n",
            "5/4\n"
          ]
        }
      ],
      "execution_count": 19,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from decimal import Decimal\n",
        "\n",
        "f = (1/4, 1/2, 3/4, 7/2)\n",
        "for the_fraction in f:\n",
        "    print(Decimal(the_fraction))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.25\n",
            "0.5\n",
            "0.75\n",
            "3.5\n"
          ]
        }
      ],
      "execution_count": 20,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Fraction(1,7) + Fraction(2,7) "
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 21,
          "data": {
            "text/plain": [
              "Fraction(3, 7)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 21,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Fraction(1/2) + Fraction(1/4) "
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 22,
          "data": {
            "text/plain": [
              "Fraction(3, 4)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 22,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Fraction(1/2)  + 6 * 3"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 23,
          "data": {
            "text/plain": [
              "Fraction(37, 2)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 23,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "Fraction(1/2) * Fraction(1/4) "
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 24,
          "data": {
            "text/plain": [
              "Fraction(1, 8)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 24,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Complex Numbers"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# For complex number use \"j\" instead of \"i\"\n",
        "# Example complex number is \"6 + 3i\";however, in Python as \"6 + 3j\"\n",
        "a = 4 + 2i # Does not work\n",
        "type(a)"
      ],
      "outputs": [
        {
          "output_type": "error",
          "ename": "SyntaxError",
          "evalue": "invalid syntax (<ipython-input-25-deebe17d43d6>, line 3)",
          "traceback": [
            "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-25-deebe17d43d6>\"\u001b[1;36m, line \u001b[1;32m3\u001b[0m\n\u001b[1;33m    a = 4 + 2i # Does not work\u001b[0m\n\u001b[1;37m             ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
          ]
        }
      ],
      "execution_count": 25,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = 4 + 2j\n",
        "type(a)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 26,
          "data": {
            "text/plain": [
              "complex"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 26,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = complex(4, 8)\n",
        "print(\"Complex Number:\", a)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Complex Number: (4+8j)\n"
          ]
        }
      ],
      "execution_count": 27,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "b = 2 + 2j\n",
        "c = 3 + 3j "
      ],
      "outputs": [],
      "execution_count": 28,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a + b"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 29,
          "data": {
            "text/plain": [
              "(6+10j)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 29,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a - b"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 30,
          "data": {
            "text/plain": [
              "(2+6j)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 30,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a * b"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 31,
          "data": {
            "text/plain": [
              "(-8+24j)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 31,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a / b"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 32,
          "data": {
            "text/plain": [
              "(3+1j)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 32,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Show which number is real and imaginary numbers\n",
        "print(\"Real number:\", a.real)\n",
        "print(\"Imaginary number:\", a.imag)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Real number: 4.0\n",
            "Imaginary number: 8.0\n"
          ]
        }
      ],
      "execution_count": 33,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sympy import *\n",
        "\n",
        "x = Symbol('x')\n",
        "y = Symbol('y')\n",
        "z = Symbol('z')"
      ],
      "outputs": [],
      "execution_count": 34,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = x*y + x*y\n",
        "a"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 35,
          "data": {
            "text/plain": [
              "2*x*y"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 35,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "c = (x + 6)*(x + 4)\n",
        "c"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 36,
          "data": {
            "text/plain": [
              "(x + 4)*(x + 6)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 36,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Expand the factor\n",
        "expand(c)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 37,
          "data": {
            "text/plain": [
              "x**2 + 10*x + 24"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 37,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "d = (x+y)**2\n",
        "expand(d)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 38,
          "data": {
            "text/plain": [
              "x**2 + 2*x*y + y**2"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 38,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "e = (x-y)**2\n",
        "expand(e)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 39,
          "data": {
            "text/plain": [
              "x**2 - 2*x*y + y**2"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 39,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "g = (x+y)**3\n",
        "expand(g)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 40,
          "data": {
            "text/plain": [
              "x**3 + 3*x**2*y + 3*x*y**2 + y**3"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 40,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sympy import pprint # Shows math expression\n",
        "pprint(g)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "       3\n",
            "(x + y) \n"
          ]
        }
      ],
      "execution_count": 41,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "u = 3*x**3 + 6*x*y - 3*y**3\n",
        "pprint(u)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   3              3\n",
            "3⋅x  + 6⋅x⋅y - 3⋅y \n"
          ]
        }
      ],
      "execution_count": 42,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from math import sqrt\n",
        "import cmath # has complex number\n",
        "# Quandratic Formula\n",
        "# https://en.wikipedia.org/wiki/Quadratic_formula\n",
        "# General Equation ax^2 + bx + c = 0\n",
        "# x = -b + sqrt(b**2 - 4ac) / 2a\n",
        "# x = -b - sqrt(b**2 - 4ac) / 2a\n",
        "a = 2\n",
        "b = 4\n",
        "c = 8\n",
        "\n",
        "# Check if the discriminant is positive, negative, or zero\n",
        "d = b**2-4*a*c # discriminant\n",
        "\n",
        "if d < 0:\n",
        "    print(\"No Solutions!\") # It has imaginary number\n",
        "elif d == 0:\n",
        "    x = -b / (2*a)\n",
        "    print(\"One solution:\", x) # Same solutions\n",
        "else:\n",
        "    x1 = (-b+sqrt((b**2)-(4*(a*c))))/(2*a)\n",
        "    x2 = (-b-sqrt((b**2)-(4*(a*c))))/(2*a)\n",
        "    print(\"Two solutions: \", x1, \" and\", x2)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "No Solutions!\n"
          ]
        }
      ],
      "execution_count": 43,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = 9\n",
        "b = 12\n",
        "c = 4\n",
        "d = b**2-4*a*c # discriminant\n",
        "\n",
        "if d < 0:\n",
        "    print(\"No Solutions!\")\n",
        "elif d == 0:\n",
        "    x = -b / (2*a)\n",
        "    print(\"One solution:\", x)\n",
        "else:\n",
        "    x1 = (-b+sqrt((b**2)-(4*(a*c))))/(2*a)\n",
        "    x2 = (-b-sqrt((b**2)-(4*(a*c))))/(2*a)\n",
        "    print(\"Two solutions: \", x1, \" and\", x2)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "One solution: -0.6666666666666666\n"
          ]
        }
      ],
      "execution_count": 44,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "a = 1\n",
        "b = 4\n",
        "c = 3\n",
        "d = b**2-4*a*c # discriminant\n",
        "\n",
        "if d < 0:\n",
        "    print(\"No Solutions!\")\n",
        "elif d == 0:\n",
        "    x = -b / (2*a)\n",
        "    print(\"One solution:\", x)\n",
        "else:\n",
        "    x1 = (-b+sqrt((b**2)-(4*(a*c))))/(2*a)\n",
        "    x2 = (-b-sqrt((b**2)-(4*(a*c))))/(2*a)\n",
        "    print(\"Two solutions: \", x1, \" and\", x2)"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Two solutions:  -1.0  and -3.0\n"
          ]
        }
      ],
      "execution_count": 45,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# This shows real and imaginary numbers\n",
        "\n",
        "a = 3\n",
        "b = 4\n",
        "c = 2\n",
        "d = b**2-4*a*c # discriminant\n",
        "\n",
        "if d < 0:\n",
        "    x1=(-b+cmath.sqrt(d))/(2*a)\n",
        "    x2=(-b-cmath.sqrt(d))/(2*a)\n",
        "    print(\"Complex Number\")\n",
        "    print(\"x1=\",x1,\" and x2=\",x2)\n",
        "elif d > 0:\n",
        "    x1=(-b+sqrt(d))/(2*a)\n",
        "    x2=(-b-sqrt(d))/(2*a)\n",
        "    print(\"Real Number\")\n",
        "    print(\"x1=\",x1,\" and x2=\",x2)\n",
        "elif d==0:\n",
        "    x=-b/(2*a)\n",
        "    print(\"Equal to Zero\" )\n",
        "    print(\"x=\",x)\n",
        "else: \n",
        "    print(\"This is NOT Quadratic Equation!\")"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Complex Number\n",
            "x1= (-0.6666666666666666+0.47140452079103173j)  and x2= (-0.6666666666666666-0.47140452079103173j)\n"
          ]
        }
      ],
      "execution_count": 46,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "a = 3\n",
        "b = 4\n",
        "c = 2\n",
        "d = b**2-4*a*c # discriminant\n",
        "\n",
        "if d < 0: \n",
        "    x1=(-b+cmath.sqrt(d))/(2*a)\n",
        "    x2=(-b-cmath.sqrt(d))/(2*a)\n",
        "    print(\"Complex Number\")\n",
        "    print(\"x1=\",x1.real, x1.imag,\"and x2=\",x2.real, x2.imag)\n",
        "elif d > 0:\n",
        "    x1=(-b+sqrt(d))/(2*a)\n",
        "    x2=(-b-sqrt(d))/(2*a)\n",
        "    print(\"Real Number\")\n",
        "    print(\"x1=\",x1,\" and x2=\",x2)\n",
        "elif d==0:\n",
        "    x=-b/(2*a)\n",
        "    print(\"Equal to Zero\" )\n",
        "    print(\"x=\",x)\n",
        "else: \n",
        "    print(\"This is NOT Quadratic Equation!\")"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Complex Number\n",
            "x1= -0.6666666666666666 0.47140452079103173 and x2= -0.6666666666666666 -0.47140452079103173\n"
          ]
        }
      ],
      "execution_count": 47,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Graphing"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt"
      ],
      "outputs": [],
      "execution_count": 48,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "y = [1,2,3,4,5,6]   # List of numbers\n",
        "plt.plot(y)         # Plot graph\n",
        "plt.show()          # Show the plot"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 49,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Parabola\n",
        "a = []\n",
        "b = []\n",
        "for x in range(-20,20,1):\n",
        "    y=x**2\n",
        "    a.append(x)\n",
        "    b.append(y)\n",
        "\n",
        "plt.plot(a,b)\n",
        "plt.show()"
      ],
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": [
              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\n"
            ],
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 50,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Trignometry \n",
        "import math\n",
        "\n",
        "def cos(x):\n",
        "    return cos(radians(x))\n",
        "def sin(x):\n",
        "    return sin(radians(x))\n",
        "def tan(x):\n",
        "    return tan(radians(x))\n",
        "def arc_tan(x):\n",
        "    return math.degrees(atan(x))\n",
        "def arc_sine(x):\n",
        "    return math.degrees(asin(x))\n",
        "def arc_cos(x):\n",
        "    return math.degrees(acos(x))\n",
        "\n",
        "print(\"Radians\")\n",
        "print(math.cos(180))\n",
        "print(math.sin(90))\n",
        "print(math.tan(45))\n",
        "print(\"Degrees\")\n",
        "print(arc_tan(1))\n",
        "print(arc_sine(1))\n",
        "print(arc_cos(1))"
      ],
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Radians\n",
            "-0.5984600690578581\n",
            "0.8939966636005579\n",
            "1.6197751905438615\n",
            "Degrees\n",
            "45.0\n",
            "90.0\n",
            "0.0\n"
          ]
        }
      ],
      "execution_count": 51,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    }
  ],
  "metadata": {
    "kernel_info": {
      "name": "python3"
    },
    "kernelspec": {
      "name": "python3",
      "language": "python",
      "display_name": "Python 3"
    },
    "language_info": {
      "nbconvert_exporter": "python",
      "name": "python",
      "pygments_lexer": "ipython3",
      "mimetype": "text/x-python",
      "file_extension": ".py",
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "version": "3.5.5"
    },
    "nteract": {
      "version": "0.11.7"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 4
}