When I run dot(a,b) in MATLAB, I get a very different number than $\sum a_i \times b_i$, but is that not how one takes a dot product? For instance:
A = [1+i 1-i -1+i -1-i];
B = [3-4i 6-2i 1+2i 4+3i];
dot(A,B)
% => 1.0000 - 5.0000i
A(1)*B(1)+A(2)*B(2)+A(3)*B(3)+A(4)*B(4)
% => 7.0000 -17.0000i
Best Answer
There is a different definition when you work with complex vectors. The dot product for complex vectors is defined as: $$\mathbf{A}\cdot\mathbf{B}=\sum_i a_i\overline{b_i}$$ Maybe this link could help: Complex dot product