9-numbers.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## int\n",
    "\n",
    "Python allows us to store numbers in 4 bases"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "split",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "| <font size=5>Number</font> | <font size=5>Base</font> |\n",
    "| --- | --- |\n",
    "| <font size=5>12</font> | <font size=5>decimal</font> |\n",
    "| <font size=5>0b1100</font> | <font size=5>binary</font> |\n",
    "| <font size=5>0o14</font> | <font size=5>octal</font> |\n",
    "| <font size=5>0xC</font> | <font size=5>hexadecimal</font> |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d = 12\n",
      "b = 12\n",
      "o = 12\n",
      "h = 12\n"
     ]
    }
   ],
   "source": [
    "d = 12\n",
    "print('d =', d)\n",
    "\n",
    "b = 0b1100\n",
    "print('b =', b)\n",
    "\n",
    "o = 0o14\n",
    "print('o =', o)\n",
    "\n",
    "h = 0xC\n",
    "print('h =', h)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### We can find the type of a variable in Python using the type() function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "type of x = <class 'int'>\n",
      "type of y = <class 'int'>\n"
     ]
    }
   ],
   "source": [
    "x = 123\n",
    "print('type of x =', type(x))\n",
    "\n",
    "y = 0b1010\n",
    "print('type of y =', type(y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Converting to other bases from decimal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "x = 123"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Decimal to Binary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0b1111011'"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bin(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Decimal to Octal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0o173'"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "oct(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Decimal to Hexadecimal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "cell_style": "center",
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0x7b'"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hex(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Converting a string to an integer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12342\n",
      "<class 'int'>\n"
     ]
    }
   ],
   "source": [
    "s = '12342'\n",
    "n = int(s)\n",
    "print(n)\n",
    "print(type(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Converting to decimal from other bases\n",
    "### We can convert a string to an integer if the string is a valid number in any base\n",
    "\n",
    "\n",
    "```java\n",
    "value = int(<number-in-base-b>, b) \n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "50\n"
     ]
    }
   ],
   "source": [
    "b = '110010'\n",
    "x = int(b, 2)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "76532\n"
     ]
    }
   ],
   "source": [
    "x = int('12af4', 16)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12\n"
     ]
    }
   ],
   "source": [
    "x = int('14', 8)\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on class int in module builtins:\n",
      "\n",
      "class int(object)\n",
      " |  int([x]) -> integer\n",
      " |  int(x, base=10) -> integer\n",
      " |  \n",
      " |  Convert a number or string to an integer, or return 0 if no arguments\n",
      " |  are given.  If x is a number, return x.__int__().  For floating point\n",
      " |  numbers, this truncates towards zero.\n",
      " |  \n",
      " |  If x is not a number or if base is given, then x must be a string,\n",
      " |  bytes, or bytearray instance representing an integer literal in the\n",
      " |  given base.  The literal can be preceded by '+' or '-' and be surrounded\n",
      " |  by whitespace.  The base defaults to 10.  Valid bases are 0 and 2-36.\n",
      " |  Base 0 means to interpret the base from the string as an integer literal.\n",
      " |  >>> int('0b100', base=0)\n",
      " |  4\n",
      " |  \n",
      " |  Methods defined here:\n",
      " |  \n",
      " |  __abs__(self, /)\n",
      " |      abs(self)\n",
      " |  \n",
      " |  __add__(self, value, /)\n",
      " |      Return self+value.\n",
      " |  \n",
      " |  __and__(self, value, /)\n",
      " |      Return self&value.\n",
      " |  \n",
      " |  __bool__(self, /)\n",
      " |      self != 0\n",
      " |  \n",
      " |  __ceil__(...)\n",
      " |      Ceiling of an Integral returns itself.\n",
      " |  \n",
      " |  __divmod__(self, value, /)\n",
      " |      Return divmod(self, value).\n",
      " |  \n",
      " |  __eq__(self, value, /)\n",
      " |      Return self==value.\n",
      " |  \n",
      " |  __float__(self, /)\n",
      " |      float(self)\n",
      " |  \n",
      " |  __floor__(...)\n",
      " |      Flooring an Integral returns itself.\n",
      " |  \n",
      " |  __floordiv__(self, value, /)\n",
      " |      Return self//value.\n",
      " |  \n",
      " |  __format__(self, format_spec, /)\n",
      " |      Default object formatter.\n",
      " |  \n",
      " |  __ge__(self, value, /)\n",
      " |      Return self>=value.\n",
      " |  \n",
      " |  __getattribute__(self, name, /)\n",
      " |      Return getattr(self, name).\n",
      " |  \n",
      " |  __getnewargs__(self, /)\n",
      " |  \n",
      " |  __gt__(self, value, /)\n",
      " |      Return self>value.\n",
      " |  \n",
      " |  __hash__(self, /)\n",
      " |      Return hash(self).\n",
      " |  \n",
      " |  __index__(self, /)\n",
      " |      Return self converted to an integer, if self is suitable for use as an index into a list.\n",
      " |  \n",
      " |  __int__(self, /)\n",
      " |      int(self)\n",
      " |  \n",
      " |  __invert__(self, /)\n",
      " |      ~self\n",
      " |  \n",
      " |  __le__(self, value, /)\n",
      " |      Return self<=value.\n",
      " |  \n",
      " |  __lshift__(self, value, /)\n",
      " |      Return self<<value.\n",
      " |  \n",
      " |  __lt__(self, value, /)\n",
      " |      Return self<value.\n",
      " |  \n",
      " |  __mod__(self, value, /)\n",
      " |      Return self%value.\n",
      " |  \n",
      " |  __mul__(self, value, /)\n",
      " |      Return self*value.\n",
      " |  \n",
      " |  __ne__(self, value, /)\n",
      " |      Return self!=value.\n",
      " |  \n",
      " |  __neg__(self, /)\n",
      " |      -self\n",
      " |  \n",
      " |  __or__(self, value, /)\n",
      " |      Return self|value.\n",
      " |  \n",
      " |  __pos__(self, /)\n",
      " |      +self\n",
      " |  \n",
      " |  __pow__(self, value, mod=None, /)\n",
      " |      Return pow(self, value, mod).\n",
      " |  \n",
      " |  __radd__(self, value, /)\n",
      " |      Return value+self.\n",
      " |  \n",
      " |  __rand__(self, value, /)\n",
      " |      Return value&self.\n",
      " |  \n",
      " |  __rdivmod__(self, value, /)\n",
      " |      Return divmod(value, self).\n",
      " |  \n",
      " |  __repr__(self, /)\n",
      " |      Return repr(self).\n",
      " |  \n",
      " |  __rfloordiv__(self, value, /)\n",
      " |      Return value//self.\n",
      " |  \n",
      " |  __rlshift__(self, value, /)\n",
      " |      Return value<<self.\n",
      " |  \n",
      " |  __rmod__(self, value, /)\n",
      " |      Return value%self.\n",
      " |  \n",
      " |  __rmul__(self, value, /)\n",
      " |      Return value*self.\n",
      " |  \n",
      " |  __ror__(self, value, /)\n",
      " |      Return value|self.\n",
      " |  \n",
      " |  __round__(...)\n",
      " |      Rounding an Integral returns itself.\n",
      " |      Rounding with an ndigits argument also returns an integer.\n",
      " |  \n",
      " |  __rpow__(self, value, mod=None, /)\n",
      " |      Return pow(value, self, mod).\n",
      " |  \n",
      " |  __rrshift__(self, value, /)\n",
      " |      Return value>>self.\n",
      " |  \n",
      " |  __rshift__(self, value, /)\n",
      " |      Return self>>value.\n",
      " |  \n",
      " |  __rsub__(self, value, /)\n",
      " |      Return value-self.\n",
      " |  \n",
      " |  __rtruediv__(self, value, /)\n",
      " |      Return value/self.\n",
      " |  \n",
      " |  __rxor__(self, value, /)\n",
      " |      Return value^self.\n",
      " |  \n",
      " |  __sizeof__(self, /)\n",
      " |      Returns size in memory, in bytes.\n",
      " |  \n",
      " |  __str__(self, /)\n",
      " |      Return str(self).\n",
      " |  \n",
      " |  __sub__(self, value, /)\n",
      " |      Return self-value.\n",
      " |  \n",
      " |  __truediv__(self, value, /)\n",
      " |      Return self/value.\n",
      " |  \n",
      " |  __trunc__(...)\n",
      " |      Truncating an Integral returns itself.\n",
      " |  \n",
      " |  __xor__(self, value, /)\n",
      " |      Return self^value.\n",
      " |  \n",
      " |  bit_length(self, /)\n",
      " |      Number of bits necessary to represent self in binary.\n",
      " |      \n",
      " |      >>> bin(37)\n",
      " |      '0b100101'\n",
      " |      >>> (37).bit_length()\n",
      " |      6\n",
      " |  \n",
      " |  conjugate(...)\n",
      " |      Returns self, the complex conjugate of any int.\n",
      " |  \n",
      " |  to_bytes(self, /, length, byteorder, *, signed=False)\n",
      " |      Return an array of bytes representing an integer.\n",
      " |      \n",
      " |      length\n",
      " |        Length of bytes object to use.  An OverflowError is raised if the\n",
      " |        integer is not representable with the given number of bytes.\n",
      " |      byteorder\n",
      " |        The byte order used to represent the integer.  If byteorder is 'big',\n",
      " |        the most significant byte is at the beginning of the byte array.  If\n",
      " |        byteorder is 'little', the most significant byte is at the end of the\n",
      " |        byte array.  To request the native byte order of the host system, use\n",
      " |        `sys.byteorder' as the byte order value.\n",
      " |      signed\n",
      " |        Determines whether two's complement is used to represent the integer.\n",
      " |        If signed is False and a negative integer is given, an OverflowError\n",
      " |        is raised.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Class methods defined here:\n",
      " |  \n",
      " |  from_bytes(bytes, byteorder, *, signed=False) from builtins.type\n",
      " |      Return the integer represented by the given array of bytes.\n",
      " |      \n",
      " |      bytes\n",
      " |        Holds the array of bytes to convert.  The argument must either\n",
      " |        support the buffer protocol or be an iterable object producing bytes.\n",
      " |        Bytes and bytearray are examples of built-in objects that support the\n",
      " |        buffer protocol.\n",
      " |      byteorder\n",
      " |        The byte order used to represent the integer.  If byteorder is 'big',\n",
      " |        the most significant byte is at the beginning of the byte array.  If\n",
      " |        byteorder is 'little', the most significant byte is at the end of the\n",
      " |        byte array.  To request the native byte order of the host system, use\n",
      " |        `sys.byteorder' as the byte order value.\n",
      " |      signed\n",
      " |        Indicates whether two's complement is used to represent the integer.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Static methods defined here:\n",
      " |  \n",
      " |  __new__(*args, **kwargs) from builtins.type\n",
      " |      Create and return a new object.  See help(type) for accurate signature.\n",
      " |  \n",
      " |  ----------------------------------------------------------------------\n",
      " |  Data descriptors defined here:\n",
      " |  \n",
      " |  denominator\n",
      " |      the denominator of a rational number in lowest terms\n",
      " |  \n",
      " |  imag\n",
      " |      the imaginary part of a complex number\n",
      " |  \n",
      " |  numerator\n",
      " |      the numerator of a rational number in lowest terms\n",
      " |  \n",
      " |  real\n",
      " |      the real part of a complex number\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1010"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int('1010', 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int('0b1010', 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "11259375"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int('0xABCDEF', 16)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int('0o14', 8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## float"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Converting a string to float"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12.453\n",
      "<class 'float'>\n"
     ]
    }
   ],
   "source": [
    "s = '12.453'\n",
    "f = float(s)\n",
    "print(f)\n",
    "print(type(f))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Get the fraction from a floating point value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "numerator = 11\n",
      "denominator = 2\n"
     ]
    }
   ],
   "source": [
    "f = 5.5\n",
    "numerator, denominator = f.as_integer_ratio()\n",
    "print('numerator =', numerator)\n",
    "print('denominator =', denominator)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Check if a float value is an integer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.3 is an integer: False\n",
      "4.0 is an integer: True\n"
     ]
    }
   ],
   "source": [
    "a, b = 2.3, 4.0\n",
    "print(a, 'is an integer:', a.is_integer())\n",
    "print(b, 'is an integer:', b.is_integer())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## complex"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(5+7j)\n",
      "<class 'complex'>\n",
      "real part = 5.0\n",
      "imaginary part = 7.0\n"
     ]
    }
   ],
   "source": [
    "c = 5 + 7j\n",
    "print(c)\n",
    "print(type(c))\n",
    "print('real part =', c.real)\n",
    "print('imaginary part =', c.imag)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Complex number from real and imag variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(12+4j)\n"
     ]
    }
   ],
   "source": [
    "re = 12\n",
    "im = 4\n",
    "c = complex(re, im)\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Absolute value of a complex number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distance of (12+4j) from the origin = 12.649110640673518\n"
     ]
    }
   ],
   "source": [
    "print('Distance of', c, 'from the origin =', abs(c))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Conjugate of a complex number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2+3j)\n",
      "(2-3j)\n"
     ]
    }
   ],
   "source": [
    "c = 2 + 3j\n",
    "c_ = c.conjugate()\n",
    "print(c)\n",
    "print(c_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### We can perform all sorts of operations on complex numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "c1 = 2 + 3j\n",
    "c2 = 3 + 2j"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2+3j) + (3+2j) = (5+5j)\n",
      "(2+3j) - (3+2j) = (-1+1j)\n",
      "(2+3j) * (3+2j) = 13j\n",
      "(2+3j) / (3+2j) = (0.9230769230769231+0.38461538461538464j)\n"
     ]
    }
   ],
   "source": [
    "print(f'{c1} + {c2} = {c1 + c2}')\n",
    "print(f'{c1} - {c2} = {c1 - c2}')\n",
    "print(f'{c1} * {c2} = {c1 * c2}')\n",
    "print(f'{c1} / {c2} = {c1 / c2}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![questions.jpg](img/questions.jpg)"
   ]
  }
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