Max Intensity of 2 Waves: E^2(E_01 +- E_02)

[fluidistic]

Homework Statement

Show that the maximum intensity of 2 waves is worth $$(E_{01}+E_{02})^2$$ while for 2 waves out of phase by pi rad, it's worth $$(E_{01}-E_{02})^2$$.

Homework Equations

Not sure about intensity. According to my notes it's worth $$(U_1+U_2)(U_1+U_2)*$$ where * denotes the complex conjugate. And $$U(x)=\sqrt{\frac{2}{\eta}}E(x)$$.
Also $$\eta=\frac{\sqrt{\frac{\mu _0}{\varepsilon _0}}}{n}$$ where n is the refractive index of the medium. Is there some easier formula for the intensity that I could use?

The Attempt at a Solution

As they don't say anything if the 2 waves have the same frequency, I think that indeed they have the same frequency otherwise it's senseless to talk of a phase. Am I right?

 

[aim1732]

If we talk of superposition of waves a phasor treatment provides
A_r² = A₁² + A₂² + 2A₁A₂cosT
where T is the phase difference. Now knowing that intensity is proportional to amplitude squared and using conditions for constructive and destructive interference you can easily show the required results.