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.
a) I can see what you have done but it seems so convoluted; how would I have known to do that and why did you choose (did you choose it? or work it out somehow?)
b) I didn't understand the transition from line 3-4 (the jump from |...| to \sqrt...). Everythign leading up to it and following it is fine, just that step.