(adsbygoogle = window.adsbygoogle || []).push({}); 1. Let z be a complex variable. Describe the set of all z satisfying |z^2-z|<1.[\b]

I have a `brute force' solution, but it's really messy. Without a graphing utility, it would be nearly impossible to graph.

I just computed |z^2-z| in terms of x and y, and solved |z^2-z|=1 in this setting. The points inside this curve, then, satisfy the inequality.

It seems like I'm missing a more elegant solution, but I can't see it.

I thought I might be onto something when I did a change of variables and put the expression into the form |u^2-1/4|<1, but that didn't seem to help much.

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# Homework Help: Complex analysis, deceptively tricky problem.

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