I'm trying to sketch the following sets in the complex plane:

For

I found the real part of

by setting

and got:

I then set this = 1 to try and graph something from which I can determine the values that are < 1:

So I would have the top half of a circle starting at (0,0) and ending at (0,1), so my set would be drawn to represent [0,1) right?

The answer I have has a circle though with the equation

and I'm not sure how this point was achieved?

b) I'm not sure how to proceed since

is abitrary but

is defined and I can plot it at (0,1), so I don't see how I can compare them.

Thanks