(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

1) Where is [tex]f(z)=\frac{sin(z)}{z^{3}+1}[/tex] differentiable? Analytic?

2) Solve the equation [tex]Log(z)=i\frac{3\pi}{2}[/tex]

2. Relevant equations

none really...

3. The attempt at a solution

For #1 I started out trying to expand this with [tex]z=x+iy[/tex], but it got extremely messy... so, I simply said that because [tex]sin(z)[/tex] is everywhere analytic, then [tex]f(z)[/tex] will only be non-diff'able were [tex]f'(z)[/tex] (which I got by simply differentiating wrt z) has poles... ie, at [tex]z=-1[/tex], [tex]z=\frac{1}{2}+i\frac{\sqrt{3}}{2}[/tex], and [tex]z=\frac{1}{2}-i\frac{\sqrt{3}}{2}[/tex].

I find my reasoning a little flimsy, is there something i;m missing?

For #2... this looked easy, I did this:

[tex]exp(Log(z))=exp(i\frac{3\pi}{2})[/tex]

so...

[tex]z=-i[/tex]

but if i take [tex]Log(-i)[/tex] it's equal to [tex]-\frac{\pi}{2}[/tex]...

now, this seems like the same thing to me... but my text says no solution... im not sure why?

any help would really be appreciated...

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Two complex analysis questions

**Physics Forums | Science Articles, Homework Help, Discussion**