Raising Complex Numbers to nth power.
I'm currently working on a little project that will require me to iterate over complex numbers in order to work out if they belong in a set. To give a bit of background it's the Mandelbrot set using the function Z = Z^2 + C where C is the given co-ordinate represented as a Complex number.
Z = (1 +3i)^2
Therfore Z = (-8 + 6i)
The next iteration....
Z = (-8 + 6i)^2
Now Z = (28-96i)
I'm failing to see the step by step methodology for doing these raises to the power of 2. All the resources I've found provide generic functional references rather than broken down steps.
If anyone could shed some light on this I would be most appreciative.
Another way to do it is....
To raze a complex number to n:th power.
Usually that is done by "de Movires" formula.
With it you can rase numbers to any power. Without any difficullty
The idea is to first write the number in polar form and then use the formula.
Hope it helps