magnitude of complex Gaussian

Question

I know X1 and X2 are two iid Gaussian random variables each distributed according to N(0, σ2), then X = whole under root of (X1^2 + X2^2) is a Rayleigh random variable.And If we take square of this X it gives exponential Random variable. Correct me if I am wrong.

and what happen If we take single Zero mean complex complex gaussian Random variable and takes it magnitude square of real and complex parts whole under root what distribution will that follow ?

Answer 1

The magnitude of a complex random variable z=x+iy, where x and y are zero-mean Gaussian distributed will still be Rayleigh, and the square of that magnitude will be exponential.