Is the power of a complex exponential signal always zero?

Question

Is the power of a complex exponential signal always zero?

For example say I have the function

$ f(t) = Ae^{i\omega t}$

Then, I think power is defined as:

$P=\int_{-T/2}^{T/2} f^2(t) dt$

So is it such that for $f(t)=Ae^{i\omega t}$, $P=0$?

Answer 1

Hint $$ \begin{split} \frac{P}{A^2} = \int_{-T/2}^{T/2} e^{2i\omega t} dt &= \int_{-T/2}^{T/2} \cos (2\omega t) + i \sin(2\omega t) dt \\ &= \left. \frac{\sin(2\omega t) - i \cos (2\omega t)}{2i\omega} \right|_{-T/2}^{T/2} \end{split} $$ Remember that sine is odd, but cosine is even. Can you finish the problem?