We can express any circle in the complex plane as |z-a|=k|z-b| where a and b are distinct complex numbers, k > 0 and [itex]k \not= 1.[/itex](adsbygoogle = window.adsbygoogle || []).push({});

Is there an elegant way of showing this fundamental property of the complex plane to be true?

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# Every circle has form |z-a|=k|z-b|

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