# Is it possible to perform basic operations on complex numbers in polar form?

##### 1 Answer

Yes, of course.

*Polar* form is very convenient to multiply complex numbers.

Assume we have two complex numbers in *polar* form:

Then their product is

Performing multiplication on the right, replacing

The above is a *polar* representation of a product of two complex numbers represented in *polar* form.

Raising to any real power is also very convenient in *polar* form as this operation is an extension of multiplication:

Addition of complex numbers is much more convenient in *canonical* form *polar* to *canonical*, add and then convert the result back to *polar* form.

The first step (getting a sum in *canonical* form) results is

Converting this to a *polar* form can be performed according to general rule of obtaining *modulus* (*absolute value*) and *argument* (*phase*) of a complex number represented as

This general rule states that

angle

(it's not defined only if both

Alternatively, we can use these equations to define angle

If