Generate Complex White Gaussian Noise in MATLAB
If you want a Circular Complex Gaussian Noise (Independent):

vComplexNoise = sqrt(noiseVar / 2) * (randn(1, numSamples) + (1i * randn(1, numSamples)))


For correlated noise you'll need to define the Co Variance Matrix and use Cholesky Decomposition.

Update

Following @Stanley Pawlukiewicz advise, run the following code:

numSamples = 100000;
noiseVar   = 4;

mA = sqrt(noiseVar / 2) * (randn(numSamples, 1) + (1i * randn(numSamples, 1)));

var(mA)


You should see result which is very close to noiseVar on the screen.