Here's a problem I ran into in complex analysis. Given z = x + iy and w = u + iv, I need to find all w such that w² = z. It reduces to solving this system: x = u² - v² y = 2uv My professor mentioned that we should try to deal with the problem in at least two cases: y = 0, and y does not equal 0 (perhaps the second case should also be split up into a few cases). But beyond the y = 0 case, I'm stuck. Can anyone help?