Solve:
I tried writing it like this:
That leaves us with: , but that didn't help much.
That seems to be more solutions than what the textbook says though. This is how I "solved" it, but I'm not sure everything I've done is correct, and I seem to be missing some solutions. I'm especially confused about taking the square root of a complex number, and when you can factor out complex numbers from square roots.
I know that this isn't true in general if z and w are complex numbers: . It's often useful to factor out from square roots though, so how do you know when you can do it?