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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: 10,325
Registered: 7/15/05
Re: real parts of powers
Posted: Feb 14, 2014 6:34 PM
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Still another revision (a simplification) ...

Sorry for the flaws in the previous versions.

Warmup problem (not hard):

Show that there exists a complex number c such that Im(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.

Conjecture:

There does not exist a complex number c such that Im(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.

quasi



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