Need a bit of help with this please.
From z = x + iy to w = u + iv, transformation T given by w = 1/z. Show that the image, under T, of the line with equation x = 1/2 in the Z plane is a circle C in the w plane. Find equation of C.
I can't get to first base here. I can do the ones where |z| = 2, or if you have a circle in the Z plane, but I cannot formulate the x = 1/2 - the only thing I can try to do is think about making up the perpendicular bisector to simuklate the locus, such that |z| = |z +1|, but not sure if that helps or not?