# Python program to show how to define a complex class

# Importing the math module
import math

# Creating a class
class Complex:
   # Giving the parameters to the class
   def __init__(self, real, img):
      self.re = real
      self.im = img

   # Defining the method to add the numbers
   def __add__(self, comp):
      return Complex(self.re + comp.re, self.im + comp.im)

   # Defining the method to subtract the numbers
   def __sub__(self, comp):
      return Complex(self.re - comp.re, self.im - comp.im)

   # Defining the method to multiply the numbers
   def __mul__(self, comp):
      return Complex(self.re * comp.re - self.im * comp.im, self.re * comp.im + self.im * comp.re)

   # Defining the method to divide the numbers
   def __truediv__(self, comp):
      m = comp.re * comp.re + comp.im * comp.im
      return Complex((self.re * comp.re + self.im * comp.im)/m, (self.im * comp.re - self.re * comp.im)/m)

   # Giving the output
   def __str__(self):

      if self.im == 0:
         return f"{round(self.re, 2)}"
      if self.re == 0:
         return f"{round(self.im, 2)}i"
      if self.im < 0:
         return f"{round(self.re, 2)} - {round(self.im, 2)}i"
      else:
         return f"{round(self.re, 2)} + {round(self.im, 2)}i"

   # Defining the method to find the modulus of the numbers
   def mod(self):
     return math.sqrt(self.re * self.re + self.im * self.im)

# Defining a function to perform all the operations
def solve(c1, c2):
   print(c1 + c2)
   print(c1 - c2)
   print(c1 * c2)
   print(c1 / c2)

print(round(c1.mod(), 2))

print(round(c2.mod(), 2))

# Creating the complex objects
c1 = Complex(1, 4)
c2 = Complex(6, -1)

# Performing the operations
solve(c1, c2)

7.00 + 1.00i
-3.00 + 5.00i
16.00 + 11.00i
0.14 + 0.66i
3.61
5.39