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Unit Disc representation help

Show that $aB_{1}(1) = B_{|a|}(a)$ for an $a\in \mathbb{C}^{*}$

This is a remark in a book called theory of complex functions that I want to prove, but I am stuck at many things I tried:

  1. I tried to put $z=e^{i\phi}$ . That was not correct

  2. I tried to put $B_{1}(1) : |z-1|<1 $ and then multiply it with $a:= x+iy$ so: $a|z-1| < a$ but because no |a| exists in this this can not be right.

Does anybody see a way to show this equation. Tell me. Please.

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    What's the difference to [this question?](http://math.stackexchange.com/questions/77379/unit-disc-representation-help)2011-10-31

1 Answers 1