there are hundreds of paper describing random number generation, and many others describing how you can tell if you have a good (pseudo-)random number generator - i recommend particular papers by harald niederrreiter, which will explain the algorithms clearly enough to write it in any programming language - he also has a book (that i have not seen; i read earlier technical papers)

Random Number Generation and Quasi-Monte Carlo Methods

SIAM 1992

The default random number generator in a whole bunch of different programming languages is the Mersenne Twister. It has been designed to deal with many of the problems associated with simpler random number generators (e.g. number * large prime % smaller prime). There's a formula, explanation and pseudocode on the wikipedia page:

https://en.wikipedia.org/wiki/Mersenne_twister

I have never needed random complex numbers; by the way you formulated the question, might it be that you need only a random variation in phase? I wonder what kind of distribution you need.

If what you need are complex random numbers with property |z|