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I've been working on this problem but I feel like I'm over complicating it. If you have a random variable X= a*e(j*phi), where phi is uniform on the interval [0,2pi) and a is some constant, and another random variable Y= b where b is a constant. I'm looking to find the probability density function of the random variable Z=X+Y.

This is probably really simple but from what I've been trying to do, I can just take the Fourier transform of X, Fourier transform of Y multiply them, and then take the inverse Fourier of that, but it doesn't seem to work. How can I do this?