M = 10;
a = 2;

numIter = 1e7;
z1_acc = zeros(1,numIter);
for iter=1:1:numIter

    x = sqrt(a)*(1/sqrt(2))*complex(randn(M,1),randn(M,1));

    denominator = (x'*x);
    z1 = M*(x(1,1) / denominator);

    z1_acc(iter) = z1;
end

var(real(z1_acc))