Some contradiction I can't explain about e^(ix)

[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.

 

[Ahmes]

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