Found the following question:

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> On the Argand diagram $P$ represents the complex number $z$ and $Q$ the complex number $\frac{1}{z}$. If $P$ lies on the straight line $x=1$ prove that $Q$ will lie on a certain circle and find its centre and radius.
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I can visualise why this is true, as $|z| ≥ 1$, hence $\frac{1}{|z|} ≤ 1$. You can also show this graphically.

However, is there an algebraic method that shows this?