Trigonometric function and complex exponential

[asifadio]

1. Homework Statement
- multiplication of trigonometric function and complex exponential



2. Homework Equations
the question is, A_kcos(ωt) × e^-jωt



3. The Attempt at a Solution
it is, A_k/2 + (A_k/2)e^-j2ωt ?
by using cos(ωt) = 1/2e^jωt + 1/2e^-jωt

 

[Dick]

1. Homework Statement
- multiplication of trigonometric function and complex exponential



2. Homework Equations
the question is, A_kcos(ωt) × e^-jωt



3. The Attempt at a Solution
it is, A_k/2 + (A_k/2)e^-j2ωt ?
by using cos(ωt) = 1/2e^jωt + 1/2e^-jωt

Looks ok to me.

 

[asifadio]

thanks!
but if i want to convolute with some real function, f(x),
can i just take a real part of
A_k/2 + (A_k/2)e-j2ωt

which is A_k/2 + (A_k/2)(2cos(ωt))?

 

[Dick]

thanks!
but if i want to convolute with some real function, f(x),
can i just take a real part of
A_k/2 + (A_k/2)e-j2ωt

which is A_k/2 + (A_k/2)(2cos(ωt))?

I hope you mean Ak/2 + (Ak/2)(cos(2ωt)). But what makes you think you can ignore the imaginary part?