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## Homework Statement

## Homework Equations

## The Attempt at a Solution

I tried to attempt the question but I am not sure how to start it, at least for part (i).

My biggest question, I think, is how does the multiplication of a random complex number to a Fourier-Transformed signal (V(f)) have an effect on V(f)? Although the question did not specify the type of signal that has been Fourier-Transformed, I shall assume that the original signal is a cosine waveform, as shown below:

_{m}=1.

In the question, it also mentioned to visualise V(f) and cV(f) as vectors in the complex plane, but how should I do it? Are there any diagrams online that show me how to represent cV(f) and V(f) as vectors in the complex plane?

Thank you. :)