The following is a quote from the Haifa Lectures (Mendel Sachs)
But if both slits are open, the wave function for the electron penetrating screen S1 is the superposition of states, $(\psi_1 + \psi_2)$, so that the probability density for the electron wave reaching screen S2 is $\left|\psi_1 + \psi_2\right|_2 = \left|\psi_1\right|_2 + \left|\psi_2\right|_2 + (\psi_1^*\psi_2 + \psi_1\psi_2^*)$. The first two terms above are the partial probability densities that the electron will pass through slit s1 or slit s2. The third term (the cross product) is the ‘interference’ part of the scattering. It shows up on screen S2 as a diffraction pattern.
I understand that this explains the diffraction pattern produced by electrons, and I know (in a general way) what $\psi_1$ and $\psi_2$ are. However I run into trouble with the next bit of math [$\left|(\psi_1 + \psi_2)\right|_2 = \left|\psi_1\right|_2 + \left|\psi_2\right|_2 + (\psi_1^*\psi_2 + \psi_1\psi_2^*)$.] especially the last part.
Could someone please offer a guide for the mathematically challenged?