Signal average power (complex signal)

[O.J.]

Homework Statement

Evaluate the average signal power of the complex signal x(t) = e ^ jwt

Homework Equations

The Attempt at a Solution

I know how to solve this but I have a couple of questions on why we have the take the magnitude of the complex signal in the integral? Besides, does a complex signal mean anything in reality? because the way I figured it is complex analysis is just a mathematical tool to help us analyse sinusoidal signals and a signal is always a real or an imaginery part of a complex function (e ^ jwt) and can't be both.

And as such I tried evaluating the integral of e ^ jwt from 0 to To using two ways:

1. write the exponential e ^ jwt in terms of cos and j sin then square that to give cos^2 wt +j2cos (wt) sin (wt) - sin^2 wt where it evaluates to some finite value
2. square the funciton so it becomes e ^ j 2wt and write that in terms of cos and j sin where it evaluates to 0

this is too mathematical I know, but how come the two mathematically valid manipulations yield integrals with different values?

 

[O.J.]

y am i being ignored?