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Let z,z(0) be two complex numbers. It is...

Let `z,z_(0)` be two complex numbers. It is given that `abs(z)=1` and the numbers `z,z_(0),bar(z_(0)),1` and 0 are represented in an Argand diagram by the points `P,P_(0),Q,A` and the origin, respectively. Show that `/_\POP_(0)` and `/_\AOQ` are congruent. Hence, or otherwise, prove that
`abs(z-z_(0))=abs(zbar(z_(0))-1)`.

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