Complex Analysis Complex Analysis Math Forum

December 12th, 2010, 10:32 AM   #1
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[attachment=0:1uzsrvmf]Assignment picture.png[/attachment:1uzsrvmf]

Any help would be much appreciated. Thank you.
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 December 12th, 2010, 11:57 AM #2 Senior Member   Joined: Nov 2010 Posts: 502 Thanks: 0 Re: Complex Numbers Question PLEASE HELP Do you know De Moivre's formula?
 December 12th, 2010, 12:53 PM #3 Newbie   Joined: Dec 2010 Posts: 3 Thanks: 0 Re: Complex Numbers Question PLEASE HELP (e^j?)^n=e^jn? isnt it? Am i right in thinking i could use this when im square rooting the e ( essentially to the power of 1/2) when i take the modulus, i.e. when i multiply out the first expression and then do z= sqr(x^2+y^2) ?
 December 12th, 2010, 02:06 PM #4 Newbie   Joined: Dec 2010 Posts: 3 Thanks: 0 Re: Complex Numbers Question PLEASE HELP hmm its still not working, im thinking i can re-arrange sin(?)= 1/2j * (e^j? + e^-j?) and make e^-j? the subject. However whenever i try this i dont know how you end up with wT/2 in the bracket.
 December 16th, 2010, 07:05 AM #5 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Re: Complex Numbers Question PLEASE HELP $J_{0}(\omega)=\frac{1}{i\omega}\left(1-e^{-i\omega T}\right)\Rightarrow |J_{0}(\omega)|=\left|\frac{1}{i\omega}\left(1-e^{-i\omega T}\right)\right|=\frac{1}{|i\omega|}|1-e^{-i\omega T}|=$ $=\frac{1}{\omega}|1+cos(\omega T)-i \sin(\omega T)|=\frac{1}{\omega}\sqrt{(1+\cos(\omega T))^{2}+\sin^{2}(\omega T)}=\frac{1}{\omega}\sqrt{2(1+\cos(\omega T))}=\frac{\sqrt{2}}{\omega}\sqrt{1+\cos(\omega T)}=$ $=\frac{\sqrt{2}}{\omega}\sqrt{2}\sqrt{\sin^{2}\lef t(\frac{\omega T}{2}\right)}=\frac{2}{\omega}\left|\sin\left(\fra c{\omega T}{2}\right)\right|$

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