If $z$ is a point on the argand plane such that $|z-1|=1$, then $\frac{z-2}{z}$ is equal to

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Professor PC Thomas Classes · Answer

Let $z-1 = e^{i	heta} \implies z = 1+e^{i	heta}$. $\frac{z-2}{z} = \frac{e^{i	heta}-1}{e^{i	heta}+1} = i	an(	heta/2)$. By geometry, this relates to $i	an(\arg z)$.