Is it correct? It is what it is. You are creating a rotationally symmetric complex random variable, where if we define the variance to be
N = 1e7;
V = 3;
X = sqrt(V/2)*(randn(N,1) + i*randn(N,1));
Does it have zero mean? That is trivial, yes. The population mean is clearly zero, and the sample mean will approach zero as N-->inf.
Xbar = mean(X)
0.0002026 - 0.00027059i
Vbar = (X-Xbar)'*(X - Xbar)/(N-1)
As you can see, the sample variance seems to approach 3. I could spend some time to verify the expected value of that result for the population, done in symbolic form. But I can as easily just say that is is "correct".