proof for $(e^{j w_0 t}) ^2 = 1$  identity? 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?
 A: Euler's formula says that, for every real number $x$, $\mathrm e^{\mathrm i x}=\cos(x)+\mathrm i\sin(x)$. Plug $x=n\pi$ into this.
A: Let $t$ denote a real number, and start from $e^{it} = \displaystyle\lim_{n\to\infty} \left( 1+\frac{it}{n} \right)^n$. Since $1\leq \displaystyle\left(1+\frac{t^2}{n^2}\right)^n \leq \left(e^{t^2}\right)^{1/n}\to 1$, we have $|e^{it}|=1$. This $e^{it}$ lies on the unit cricle. 
Define $\sin(x), \cos(x), \tan(x) $ to be the trigonometric functions defined by points on the unit circle, not power series. Draw a picture to convince yourself that $\sin(x) \leq x \leq \tan(x) $ for small positive $x$, and $\tan(x) \leq x \leq \sin(x)$ for small negative $x$. Argue via squeeze theorem that $\tan(x) \sim x $ as $x\to 0$. 
Now note $\arg(e^{it}) = \displaystyle\lim_{n\to\infty}  n\cdot \tan^{-1}(t/n) = t$ . Thus, $e^{it}$ is the point on the unit circle whose argument is $t$, which answers your question.
Some nice side effects: 


*

*This connects the power series trig functions back to geometry quite quickly. When one starts from power series, it is not obvious that they are $2\pi $ periodic, so this is a nice way to show that.

*This allows us to avoid having to define $\pi$ as the smallest positive $x$ such that $\sin(x) =0$ or something like that - it matches with our geometric definition that $2\pi $ is the circumference of the unit circle.  

