- #1
Malgrif
- 18
- 0
Homework Statement
I want to know the steps involved in finding the magnitude of a complex exponential function. An example of the following is shown in this picture:
Homework Equations
|a+jb|=sqrt(a^2+b^2)
|x/y|=|x|/|y|
The Attempt at a Solution
For the denominator, I replaced z with e^jw and used euler identity to expand the terms.
1-2rcos(w)e^(-jw)+r^2e^(-2jw)
1-rcos(w)*(cos(w)-jsinw)+.5r^2(cos(2w)-jsin(2w))
After simplifying I get:
1-rcos^2(w)+.5r^2cos(2w) + j(rsin(w)cos(w)-.5r^2sin(2w)
from there I let a=1-r(cos^2(w)-.5r^2cos(2w)) and b=r(sin(w)cos(w)-.5rsin(2w))
and using wolfram alpha to solve for sqrt(a^2+b^2) I don't get the simplified expression shown in the picture above. Am I approaching the problem correctly?