Reply #2: Ok, I'll throw this at you on the off chance...

[LynzM]

Let me start with, I loathe proofs :) Which makes the first of these two loads of fun...

1.) Show that complex conjugate (CC(sin(iz)) = sin(CC(iz)) iff z=n*pi*i (n=0,+-1, +-2....) (sorry for the poor notation, I don't have any spiffy programs to clean it up with!) given that

sin(z) = (exp(iz) - exp(-iz))/2i

I can do a lot of algebra and get down to:

((1/exp(x)-exp(x))*(sin(-y)+sin(y)) = 0

but I don't know how that helps me, as the second part is always =0, so who cares what x is, which neither of those addresses the "iff z=n*pi*i" part, at all. *sigh*


The second one is maybe more straightforward, but I'm still stuck:

2.) Solve the equation cos(z) = sqrt(2) w/out using cos-1(z) = -ilog{z+i(1-z^2)^.5}

given cos(z) = (exp(iz)+exp(-iz))/2

again, lots of algebra winds me up with cos(x)*(exp(-y)+exp(y))= 2*sqrt(2)


Thanks for any help, thoughts, suggestions... I feel like I just got totally in over my head in this class, and a week ago I felt like I was doing okay. Eek. Anyone else is welcome to jump in, too, if you want! :hi: