Fourier Transform of v(t)=A*e(-t) for t≥0

[yoamocuy]

Homework Statement

I need to find the Fourier transform of v(t)=A*e^(-t) such that t≥0.

Homework Equations

∫v(t)*e^{(-j*2*∏*f*t)}dt,t,0,∞)

The Attempt at a Solution

∫v(t)*e^{(-j*2*∏*f*t)}dt,t,0,∞)=A/(4*f²*∏²+1)-i*(2*A*f*∏)/(4*f²*∏²+1)

the answer should be A/(1+i*2*∏*f). It seems like this problem should be straight forward so I'm wondering if I'm just missing an identity of some sort or something? This is actually only one part of the problem but I know how to get the rest of the answer once I get this part done.

 

[yoamocuy]

Ok so I realize these are the same answer, but how do I simplify complex numbers like the one I got in my answer? I've been trying to multiply it by the complex conjugate but haven't been getting much luck :/

 

[vela]

Combine the two terms and then factor the denominator.

 

[yoamocuy]

I've combined the two equations to get: (A-j*2*A*f*∏)/(1+4*f²*∏²) but it doesn't seem that the denominator can be factored at all. I can factor the numerator to get A*(1-j*2*f*∏)/(1+4*f²*∏²) but that doesn't seem to help me much yet.

 

[yoamocuy]

Oh I got it now