"In Young's double slit experiment, assuming the distance between the slits is 0.07mm and the wavelength of light used is 600 nm, when the screen is 70 cm away, what kind of interference is there."
I'm not sure what I'm being asked to determine here.
Plugging in the figures into the...
The question calls for using Cauchy's integral formula to compute the integral for Int.c z/[(z-1)(z-3i)] dz, assuming C is the loop |z-1|=3.
Taking z = 1 and f(z) = z/(z-3i), I came up with (2pi*i)/(1-3i), which seems like it could be simplified, but I'm not sure how.
Alright then, so z = (z + i)A + (z - 2i)B, then expanding gives
z = z(A + B) + i(A - 2B)
Since the LHS has no i, then A - 2B = 0, and likewise, A + B = 1
But...this is going nowhere. Where am I slipping up?
I need to find the partial fraction expansion of the integrand z/[(z-2i)(z+i)]
Just doing 1/(z-2i) + 1/(z+i) results in (2z-i)/(z-2i)(z+i).
It seems easy, but I can't figure out what to multiply by to get the correct numerator.
As part of finding the integral of z/(z^2 -1), I'm stuck on getting the partial fraction for it. 1/2 [(1/(z-1) - 1/(z+1)] gives 1/(z^2-1). What should I do to get the z in the numerator. Any hints welcome.
Cauchy integral question
The question calls for finding the integral of dz/((z-i)(z+1)) (C:|z-i|=1)
I can't figure out how to do this for (C:|z-i|=1). How does this differ from, say, (C: |z|=2)
"There are two sine waves having a phase difference of 20 degrees. After one reaches its maximum value, how much time will pass until the other reaches its maximum, assuming a frequency of 60 Hz."
Should I go about this by assuming...
sin(120pi*t) = sin(120pi(t + x) - 20)
The problem is to find the definite integral of e^2x/(e^x + e^-x) with the limits of 0 and log 2. Finding the integral was easy enough, e^x - log (1 + e^2x) , but how do I plug log 2 into this. Any hints appreciated.