Solution
= Solution
Write $z_j=x_j+iy_j$. Multiplication gives
$$
Q=x_1x_2+y_1y_2+i(y_1x_2-x_1y_2).
$$
Therefore the <real part> is the <dot product> of the corresponding <vectors>:
$$
\boxed{\Re Q=x_1x_2+y_1y_2=\mathbf v_1\cdot\mathbf v_2.}
$$
For nonzero <vectors>, this is $|z_1||z_2|\cos(\arg z_1-\arg z_2)$, measuring their alignment.