# How to multiply two complex numbers in python ?

Published: April 15, 2020

Tags: Python; cmath;

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)`
```