# Complex number problem

Discussion in 'Homework Help' started by daviddeakin, Dec 12, 2010.

1. ### daviddeakin Thread Starter Active Member

Aug 6, 2009
207
27
Hi,
can anyone help me with this problem? I have included what working I can do, but I can't see any way of even getting close to the expected answer!
Much grovelling!

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2. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
Try this for the nominator:
$1-e^{j \omega T}=\\
1-\cos( \omega T)+j\cdot \sin( \omega T)\\
\\
abs(1-\cos( \omega T)+j\cdot \sin( \omega T))=\\
\sqrt{(1-\cos( \omega T))^2 + \sin^2( \omega T)}=\\
\sqrt{1-2cos( \omega T)+\cos^2( \omega T)+\sin^2( \omega T)}$

Can you continue?
You will also need the equation $\cos(x)=2\cos^2\left( \frac{x}{2} \right) -1$.

Solve this and we 'll see the angle next.

Last edited: Dec 13, 2010
Also remember that $|z|^2 = zz^*$ is a handy relation, especially for complex exponentials (* denotes the conjugate).