Consider a class Complex that simulates the built-in complex data type. The class en- ables operations on so-called complex numbers. These are numbers of the form realPart + imag- inaryPart * i, where i has the value ?-1

Question

a) Modify the class to enable output of complex numbers in the form (realPart, imaginary-Parti), through the overloaded __str__ method.
b) Overload the multiplication operator to enable multiplication of two complex numbers as in algebra, using the equation
(a, bi) * (c, di) = (a*c - b*d, (a*d + b*c)i)
c) Overload the == operator to allow comparisons of complex numbers. [Note: (a, bi) is equal to (c, di) if a is equal to c and b is equal to d.

Answer 1

```
# Complex number class.

class Complex:
"""Complex numbers of the form realPart + imaginaryPart * i"""

def __init__( self, real = 0, imaginary = 0 ):
"""Assigns values to realPart and imaginaryPart"""

self.realPart = real
self.imaginaryPart = imaginary

def __add__( self, other ):
"""Returns the sum of two Complex instances"""

real = self.realPart + other.realPart
imaginary = self.imaginaryPart + other.imaginaryPart

# create and return new complexNumber
return Complex( real, imaginary )

def __sub__( self, other ):
"""Returns the difference of two Complex instance"""

real = self.realPart - other.realPart
imaginary = self.imaginaryPart - other.imaginaryPart

# create and return new complexNumber
return Complex( real, imaginary )

def __mul__( self, other ):
"""Returns the product of two Complex instances"""

real = self.realPart * other.realPart - \
self.imaginaryPart * other.imaginaryPart
imaginary = self.realPart * other.imaginaryPart + \
self.imaginaryPart * other.realPart

return Complex( real, imaginary )

def __str__( self ):
"""Represent Complex instance in form
( realPart, imaginaryParti )"""

return "(%d,%di)" % ( self.realPart, self.imaginaryPart )

def __eq__( self, other ):
"""Overloads equality operator"""

if self.realPart == other.realPart and \
self.imaginaryPart == other.imaginaryPart:
return 1
else:
return 0.
```
>>> c1 = Complex( 2, 3 )
>>> c2 = Complex( 1, -3 )
>>> c3 = Complex( 2, 3 )
>>> print "c1 =", c1
c1 = (2,3i)
>>> print c1 * c2
(11,-3i)
>>> if c1 == c3:
... print "c1 is equal to c3"
... else:
... print "c1 is not equal to c3"
...
c1 is equal to c3