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.