Absolute value of complex exponential Can somebody explain to me why the absolute value of a complex exponential is 1? (Or at least that's what my textbook says.) 
For example:
$$|e^{-2i}|=1, i=\sqrt {-1}$$

I would like to provide an intuitive understanding, in addition to the previous excellent answers.
Recall that a complex number in Euler’s form can be expressed as $r e^{i \theta}$, in this case, the modulus is 1 and the argument is -2. Graphically, we can visualize complex numbers of modulus 1 as points on a unit circle.
Algebraically, we say that the unitary group of degree 1 is isomorphic to the unit circle, namely $U(1) \cong S^1$
