Matlab: What is the proper way to calculate mean square error for complex numbers
The mean square error is

e = ((abs(h_e1 - h_true(1))^2) + (abs(h_e2 - h_true(2))^2) + (abs(h_e3 - h_true(3))^2))/3;


But it is tediuos! 

What if you had $1000$ terms instead of $3$? Do you want to add one by one?

Do it in the vector form for more clarity and ease of implementation:

$$\mathrm{mse}=\mathsf{E}(|\mathbf{h}-\hat{\mathbf{h}}|^2)$$

In MATLAB, you can use the function mse() 

 h_true = [ 0.7071 + 0.7071i
            0.4243 + 0.4243i
            0.2121 + 0.2121i ];

 h_e = [ 0.8100 + 0.8100i  
         0.5100 + 0.5100i  
         0.1200 + 0.1200i ];

 e = mean(abs(h_e-h_true).^2); % or eqivalently e = mse(abs(h_e-h_true));