Finding poles

Jul 2006
364
44
Find all poles of \(\displaystyle f(z)=\frac{\sin^2 z}{z^3+8i} \) and state the order of the poles.

Do I need to do a full Laurent expansion of this? Or is there an easier way?

EDIT: I guess it seems to have a pole of order 1 at \(\displaystyle 2i\)?
 
Last edited:

Drexel28

MHF Hall of Honor
Nov 2009
4,563
1,566
Berkeley, California
Find all poles of \(\displaystyle f(z)=\frac{\sin^2 z}{z^3+8i} \) and state the order of the poles.

Do I need to do a full Laurent expansion of this? Or is there an easier way?

EDIT: I guess it seems to have a pole of order 1 at \(\displaystyle 2i\)?
I would agree with your edited answer.
 
Jul 2006
364
44
I worked on this a bit more and found 3 unique poles by solving \(\displaystyle z^3=-8i\) and DeMoivre's theorem. Thanks anyhow.