Relation between intensity and amplitude

[albega]

When superposing waves in say double slit interference from two slits, I seem to have come across two approaches:
1. Sum the two waves in complex form to get the resultant amplitude, take the real part, and square to get the intensity, i.e I=[Re(A)]²
2. Sum the two waves in complex form to get the resultant complex amplitude. Then take the modulus squared to get the intensity, i.e I=AA*.
What is it that makes these two approaches give the same result. Mathematically they seem to be different to me. Also, where does the second come from? I know I=cε₀E² but this doesn't involve the modulus does it?

 

[RUber]

If you think of the complex A in the exponential form, $A = r e^{i \theta}$, then $[Re(A)]^2 =( r \cos \theta) ^2$.
Also, $AA^* = r e^{i \theta}r e^{-i \theta} =r^2$, therefore these are mathematically the same only when you are approaching head on (angle = 0 or pi).