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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),zbar_(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)=abs(zbar(z_(0))-1)`.

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