- #1
Ahmes
- 75
- 1
Let k be a real number (not necessarily an integer).
[tex]e^{i\cdot2\pi\cdot k}=\cos(2\pi k) + i\sin(2\pi k)=[/tex] some complex number on the unit circe.
BUT
[tex]e^{i\cdot2\pi\cdot k}=(e^{i2\pi})^k=1^k=1[/tex]
so if take [itex]\tilde{k}=2\pi k[/itex] then [itex]1=e^{i\tilde{k}}=[/itex]every other number on the unit circle.
How can this be explained??
Thanks.
[tex]e^{i\cdot2\pi\cdot k}=\cos(2\pi k) + i\sin(2\pi k)=[/tex] some complex number on the unit circe.
BUT
[tex]e^{i\cdot2\pi\cdot k}=(e^{i2\pi})^k=1^k=1[/tex]
so if take [itex]\tilde{k}=2\pi k[/itex] then [itex]1=e^{i\tilde{k}}=[/itex]every other number on the unit circle.
How can this be explained??
Thanks.