Upon initially looking at it, you may have no clue how to do it. This feeling is fine. You should think for a bit and see if you can think of anything to do. If you can’t think of anything to do, JUST DO SOMETHING. In this case, we may try to use the hint immediately on the |z-1| part. But after doing that we’ll likely feel lost, and unsure how to proceed from their.
Hence, we’ll try problem solving tip number 1 (understand the problem). Right now it just looks like a bunch of algebra. Let’s just plug in a number and see how it works. To do this we need to know what z satisfy the first condition, which may motivate us to draw its graph (a circle) and pick from that some points to try.
Hopefully after a bit of tinkering, you’ll come to the realisation that maybe you could just use the geometry of the circle and angles to solve the problem (which is one of the solutions). Another way to get to this same outcome is to think about what is stopping you from solving the problem immediately.
Problem solving strategy 3: What’s so difficult about this problem? Hopefully you’d say it’s the angle condition, since it’s super awkward to do algebra with. So you need an easier way to work with angles, thus motivating you to use geometry.
