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:(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Homework Help: Complex Analysis: Nonlinear system

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