Sorry to double post but I thought the other post that contained the initial question was really messy so I decided to start a new thread. Just need help with this one quesiton. Thanks.

1.) Sketch the region of the complex plane given by Im(z^2) =2 and pi/8 < arg (z) < 3pi/8

My solution: z = x + iy, so z^2 = x^2 - y^2 + 2xiy

then Im(z^2) = 2xiy = 2
2xiy = 2
xiy = 1
iy = 1/x

i sketched the general curve of a 1/x graph and included only a small portion of the curve in the first quadrant because of the angle restriction. is this correct?

thanks.