PHZ 3113 Fall 2010
Homework #6, Due Friday, October 22
i
i
1. Compute ln[ (ii ) ]. Compute ln[ i(i ) ].
2. Find all z such that cos z = i.
∞
X
1
3. Compute
(iπ − 1)n .
n!
n=0
4. In optics, the intensity of the interference between 2n + 1 sources arrayed along the y-axis
separated by distance d one from the next and radiating in phase is proportional to the
square of the amplitude
n
X
ψ=
eij∆φ ,
j=−n
where the phase difference between sources is ∆φ = kd sin θ (k = 2π/λ is the wavenumber
of the radiation, θ is angle from the x-axis). Compute the sum and determine |ψ|2 . Identify
values of θ where the amplitude has peaks.
5. Use complex numbers to sum the series
∞
X
k=0
1
sin[(2k + 1)x] e−(2k+1)y
2k + 1
for y ≥ 0. Sketch the behavior of your solution as a function of x for y → 0+ .