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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
Re: Let Z be a complex number.
Posted: Oct 27, 2013 4:48 AM
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>
> Are you sure of "> 2"?
>


sqr((x + 1)^2 + y^2) > 2 can be rewritten as
((x + 1)^2 + y^2) > 4 , <=>
x^2 + 2x + 1 +y^2 > 4 <=>
x^2 +2x + y^2 > 3 which is what we've started with.
The same goes for the other relation.



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