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!
     
  2. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    Try this for the nominator:
    1-e^{j \omega T}=\\<br />
1-\cos( \omega T)+j\cdot \sin( \omega T)\\<br />
\\<br />
abs(1-\cos( \omega T)+j\cdot \sin( \omega T))=\\<br />
\sqrt{(1-\cos( \omega T))^2 + \sin^2( \omega T)}=\\<br />
\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
  3. someonesdad

    Senior Member

    Jul 7, 2009
    1,585
    141
    Also remember that |z|^2 = zz^* is a handy relation, especially for complex exponentials (* denotes the conjugate).
     
  4. daviddeakin

    Thread Starter Active Member

    Aug 6, 2009
    207
    27
    Thanks for the pointers- I solved it in the end! Hooray!
     
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