I came across a question where the following was done:
$ (e^{jw_0t})^2 = 1. $
After some searching I realized that there was an identity that says that $e^{jn\pi} = 1$ if $n$ is even and $-1$ if $n$ is odd.
Can someone provide a proof for this identity? I am really confused as to how $e^{jn\pi} = 1$ if $n$ is even?!
thanks.
NOTE: I am guessing w0 = (2*pi) / period because we usually use cos(w0*t) notation so
After looking at the responses below, if I now use the Euler formula:
e^(j* [(2*pi) / period]) so this equals cos((2*pi) / period) + jsin((2*pi) / period)... this does not equal 1..
am I doing something wrong?