Originally Posted by
aande So I've been working on this 1 question for about an hour trying to find some sort of insight or similar question that can help me out. I've been looking for some sort of example where there is a graph of z^2.
My problem is this:
Sketch the set, s, where s = {z  z^2  1  < 1 } ... z is a complex number
I know that if it was s = {z  z  < 1 } then I would get a unit disc. And, if there were numbers inside the absolute value then it would a shift or some sort.
The closest thing I can think of is factoring the interior of the absolute value so I get conjugates but I don't see how that helps. Another thing I thought of was use the graph of z^2 bounded by a positive integer but I don't know what that looks like. I suppose I could made z = x + iy but then I might get bogged down with calculation.

the next question is
Sketch the set, s, where s = {Z  Z  > 2  Z  1  } ... Z is a complex number

Any help would be greatly appreciated.
Thank you