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Topic: real parts of powers
Replies: 9   Last Post: Feb 15, 2014 1:41 PM

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quasi

Posts: 10,188
Registered: 7/15/05
Re: real parts of powers
Posted: Feb 14, 2014 6:19 PM
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Zeit Geist wrote:
>quasi wrote:
>>
>>Warmup problem (not hard):
>>
>>Show that there exists a complex number c such that Re(c^n)
>>is nonzero for all positive integers n, and such that
>>
>> Re(c^n1) = Re(c^n2) = Re(c^n3)
>>
>>for some distinct positive integers n1,n2,n3.

>
>Are you asking for a non-real complex number c?


Not as stated.

But I missed a needed restriction which would have implied that
c is non-real.

>If not, let c = -1. For any even positive integer n, we have
>(-1)^n = 1. Similarly, for odd n, resulting in -1.


For that matter, c = 1 works.

>ZG
>
>PS. If I'm completely missing something, please be polite.
>Thank you.


Don't be silly -- I'm always polite (well, ok, not always,
but most of the time, at least when replying to non-trolls).

Thanks for alerting me to the need for a correction.

I'll try again with a revised wording of the problem in my next
reply.

quasi



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