My attempt at a solution: I simply took the cube of z, and found it to be equal to

. It would be nice if we could just factorize this by letting (-1)^(1/3) be equal to -1, thus obtaining the mentioned equation. The only problem is that (-1)^(1/3) is not defined, and could be -1 as well as

. How do I proceed from here?

My third question is: I can solve the mentioned third-degree equation, but it has three solutions. I managed to "pick" the right one (which is 1+3i) by "seeing" that z has a positive imaginary part, and a positive real part. However, I'm not very confident with my method, so I wonder if there's any better way.

I'd be grateful for your help!