# How to multiply two complex numbers in python ?

Daidalos April 15, 2020

Example of how to multiply two complex numbers in python

### Create two complex numbers in python

Let's import the module python cmath that is used to work with complex numbers

>>> import cmath


Create a first complex number z1:

>>> z1 = 1.0 + 2.0j
>>> z1
(1+2j)


of real part

>>> z1.real
1.0


and imaginary part

 >>> z1.imag
2.0


Let's also create another complex number z2:

>>> z2 = 3.0 + 5.0j
>>> z2 
(3+5j)


### Multiply the two complex numbers

To multiply z1 by z2, a solution is to use the operator *, example:

>>> z3 = z1 * z2
>>> z3
(-7+11j)


### Use the polar representation

Transform z1 in polar representation:

>>> r1,theta1 = cmath.polar(z1)
>>> r1,theta1
(2.23606797749979, 1.1071487177940904)


Transform z2 in polar representation:

>>> r2,theta2 = cmath.polar(z2)
>>> r2,theta2
(5.830951894845301, 1.0303768265243125)


Then, multiply z1 by z2 using:

>>> r3 = r1 * r2
>>> theta3 = theta1 + theta2
>>> r3,theta3
(13.038404810405298, 2.137525544318403)


Going back to cartesian representation:

>>> cmath.rect(r3,theta3)
(-6.999999999999999+11.000000000000002j)