Is it possible to perform basic operations on complex numbers in polar form?
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
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
(it's not defined only if both
Alternatively, we can use these equations to define angle