09 - Operations on Complex Numbers using Various Forms of Their Representation

The reason we delayed this until now is actually quite surprising. Operations with complex numbers are... complex. These different forms make it very easy to perform operations on complex numbers. It is the best approach to convert a complex number to a suitable form then calculating.

Complex Number Addition and Subtraction

The best way to do this is in rectangular form, where . This way, adding or subtracting complex numbers is a simple matter of adding or subtracting the real and imaginary parts respectively

Complex Number Multiplication and Division

The best way to do this is in exponential form, Euler's form, represented as , where we don't have to use complicated polynomials at all, but it becomes a simple matter of quick calculations by using the properties of the exponential, and we get

10 - Powers of i

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