If you take a look at the var documentation https://es.mathworks.com/help/matlab/ref/var.html you can see that the definition is not the same than the one you are using:
x = [1, -1, 1+1i, 1-1i];
Var1 = var(x)
Var2 = sum(abs(x-mean(x)).^2)/(numel(x)-1) %Following the definition
Var1 =
1.6667
Var2 =
1.6667
To use your definition of the variance, you have to put:
Var1 = var(x,1)
Var2 = mean(abs(x).^2)-(abs(mean(x)).^2)
Var1 =
1.2500
Var2 =
1.2500
