Let $X_1$ and $X_2$ be independent complex Gaussian random variables, $$X_1 \sim \mathcal{CN}(0,\sigma)$$ $$X_2 \sim \mathcal{CN}(0,\sigma)$$
If $X= aX_1 + bX_2$ where $a,b$ are constants then the complex Gaussian random variable $X$ is also Gaussian $$X\sim \mathcal{CN}(0,a^2\sigma+b^2\sigma)$$
My question is next, I have to find the distribution of magnitude and the square of magnitude of $X$ $$Y=|X| $$$$Z=|X|^2$$ Is the distribution Rayliegh and exponential ? If yes what are the mean and variance?
Cheers!