Helloo, is there someone who could please share their derivation of the last step for the dispersion in Q1b of the 2019 exam? I can’t manage to get an expression with cos^2 and sin^2 as they did in the solution:
Use:
e^i(ax) = sin(ax) + icos(ax)
&
|z| = sqrt(a^2+b^2) met z = a + bi
and you end up with that
|\kappa_1 + \kappa_2 \exp 2ika| = |(\kappa_1 + \kappa_2 \cos 2ka) + i\kappa_2 \sin 2ka | = \sqrt{(\kappa_1 + \kappa_2 \cos 2ka)^2 + (\kappa_2 \sin 2ka)^2}
ahhh of course thank you both!! forgot about this
1 Like