I'm struggling with this question
Show that the transformation w=z-1/z maps |z-1|=1 in the z-plane to |w|=|w-1| in the w-plane.
Any help would be much appreciated. Thanks
2026-04-04 14:48:36.1775314116
Mapping from the z-plane to the w-plane
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Hint...start by writing $$z=1+e^{i\theta}$$ and simplifying $$z-\frac 1z$$ You should end up with the real part equal to $\frac 12$ which is equivalent to the required locus