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Or is that not why |exp(-iωt)| = 1, if indeed it equals 1 at all?

More precisely, is it because √ ((cosine squared x) + (sine squared x)) = 1?

Incorporated this post in the next one...

How should I manipulate Euler's formula ?

Does |exp(-iωt)| = 1 aswell?

Thanks.

Thanks again. Going off on a tangent for a moment, do exp(iωt) and exp(-iωt) each form a circle of unit radius on an argand diagram? When I substituted the number 1 for |exp(iωt)| and again the number 1 for |exp(-iωt)|, I ended up with Fc(ω) =(√(2/∏)) x (5 / (5squared PLUS ωsquared))...

Thanks. If |exp(iωt)| = 1 and |exp(-iωt)| = 1 for all t, how do sin(ωt) and cos(ωt) vary with t, when they are functions of exp(iωt) and exp(-iωt)?

Should I use frequency shifting? The Fourier transform of f(t)cos(ωsub0t) being equal to 0.5(F(ω-ωsub0) + F(ω+ωsub0)) and the Fourier transform of exp(-5t) being 1 / (5 + iω) is the Fourier Transformation of exp(-5t)cos(ωsub0t) equal to 1 / (5 + iωsub0)? In that case the simple, final...

I only know the simple answer to the problem I asked about, but not how to produce it, which is the real issue. If you are not going to help me out with this particular problem, which I can assure you is becoming a serious distraction from the rest of the subject, could you please describe the...

Is there an altogether better approach to this problem?

For the Fourier cosine transformation (and similarly for the sine) I got this far by firstly converting cos(ωt) into 0.5(exp(iωt) + exp(-iωt)) and then multiplying by exp(-5t),

Apparently the ultimate solution is Fc(ω) = (√(2/∏))(5/5squaredωsquared) but how?

Well for the Fourier cosine transformation I end up with (1/√2∏) ( (exp((iω - 5)t)/(iω - 5)) + (exp((-iω - 5)t) / (-iω - 5)) ) evaluated over the range from 0 to ∞, but what do exp((iω - 5)t) and exp((-iω - 5)t) equal at t = ∞? . Similarly for the Fourier sine transformation. If...

Oops sorry! I forgot to mention that negative, but I still can't do the problem.