Let's say that I have two complex numbers, a and b, with different arguments. From a few "experiments" with a computer, I think that there always exists a positive integer n such that -pi/2 <= Arg(a^n) <= pi/2 and pi/2 <= Arg(b^n) <= 3pi/2.(adsbygoogle = window.adsbygoogle || []).push({});

In other words, if Arg(a) = thetaA and Arg(b) = thetaB, then there exists an n such that

-pi/2 <= n*thetaA <= pi/2 and pi/2 <= n*thetaB <= 3pi/2 up to a multiple of 2pi.

Is this true? If so, how can I start to prove it?

Thanks,

Daniel

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# Rotating two different complex numbers

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