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Topic: Let Z be a complex number. How do you (elegantly) prove that |z - 1|
> 2 implies |z^3 - 1| > 1

Replies: 11   Last Post: Oct 29, 2013 2:49 AM

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dan.ms.chaos@gmail.com

Posts: 409
Registered: 3/1/08
Let Z be a complex number. How do you (elegantly) prove that |z - 1|
> 2 implies |z^3 - 1| > 1

Posted: Oct 25, 2013 11:33 AM
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Of course the proof boils down to elementary algebra, but I'm looking for a way that avoids tedious calculations as much as possible (eg. some geometric principle) ...



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