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Prove that locus of is circle and find its centre and radius if is purely imaginary.
Prove that locus of $z$ is circle and find its centre and radius if $\frac{z-i}{z-1}$ is purely imaginary.
Given: $\frac{z-i}{z-1}$ is purely imaginary.
To show: Locus of $z$ is circle with centre $(1/2, 1/2)$ and radius $1/\sqrt{2}$.
Answer
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From ISC 2017 Mathematics Paper 1, question 9(a).