Thank you for your help, I'm sorry but I'm still stuck. I used the relevant equations to substitute w = e^(iz)to get w=0 or w=-1, so |w|=e^(-y)=0 or |w|=1, so $$e^{iz}=e^{-y}(\cos x_0 + i \sin x_0)$$ which means that $$ x_0=\pi+n2\pi $$
is this even correct? I'm sorry I'm new to complex numbers
but wouldn't I then still be using the logarithm? Since then I would have to do 1/2+p = exp( ln( 1/2+p ) ) but I'm not getting all solutions, since p is in Z and I'm not allowed to evaluate a complex logarithm?
Homework Statement
Solve the equation
$$cos(\pi e^z) = 0$$Homework Equations
I am not allowed to use the complex logarithm identities.
$$ \cos z = \frac{e^{iz}+e^{-iz}}{2} $$
$$e^{i\theta}=\cos\theta+i \sin\theta$$
The Attempt at a Solution
All I've gotten is $$\cos(\pi e^z)=0 \iff \pi...
Homework Statement
Find a function in a measurable space that is non-measurable, but |f| and f2 are measurable.
Homework Equations
None.
The Attempt at a Solution
I am trying to understand the following answer to the problem:
(source: http://math.stackexchange.com/a/1233792/413398)
I do...
Not sure about the translated term limited (from German); perhaps cut-off function?
Homework Statement
Let f be a measurable function in a measure space (\Omega, \mathcal{F}, \mu) and C>0. Show that the following function is measurable:
f_C(x) =
\left\{
\begin{array}{ll}
f(x) & \mbox{if }...