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)`

### References

Links | Site |
---|---|

Comment calculer les coordonnées polaires d'un nombre complexe en python ? | moonbooks.org |

Représentation géométrique d'un nombre complexe | bibmath.net |

cmath — Mathematical functions for complex numbers | python doc |