1. ## Mandelbrot set problem

This is high school math, not uni, but it's extension and I felt it didn't belong in the high school section.

In any case, I'm doing an assignment on fractals and I don't understand the following question:

If we write Z = x + yi and c = a + bi, show for the iterated Z (i.e. Z = Z2 + c),
Re (Z^2 + c) = x^2 – y^2 + a
i)
Im (Z^2 + c) = b + 2xy
ii)

Can someone please explain it to me?

2. Calculate z^2 + c and then pull out the real part and the imaginary part.

3. Thanks :-)