1. Feb 22, 2006

Ahmes

Let k be a real number (not necessarily an integer).
$$e^{i\cdot2\pi\cdot k}=\cos(2\pi k) + i\sin(2\pi k)=$$ some complex number on the unit circe.
BUT
$$e^{i\cdot2\pi\cdot k}=(e^{i2\pi})^k=1^k=1$$

so if take $\tilde{k}=2\pi k$ then $1=e^{i\tilde{k}}=$every other number on the unit circle.

How can this be explained??
Thanks.

2. Feb 22, 2006

Ahmes

solved... I'm an idiot.
$$1^k$$ with complex numbers are all the unit's $$k^{-1}$$ roots...