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

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Posts: 12,067
Registered: 7/15/05
Re: real parts of powers
Posted: Feb 14, 2014 6:10 PM
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giovanni wrote:
>quasi wrote:
>>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) = Re(c^n4)
>>where n1,n2,n3,n4 are distinct positive integers.

>Maybe I'm missing something.

No, you're fine.

>What about c = -1/2 + I* Sqrt(3)/2, which satisfies c^3 = 1 ?
>I think that Re(c^n) = -1/2 for all n which are not multiples
>of 3 and Re(c^n)=1 for n=3k.

Yep -- I need a further restriction.

I'll revise the problem in my next reply.

Thanks for making me aware of the issue.


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