Sin(z)=0
∴z=0 or z=kπ
When z=0,
Numerator: f(z)=z^2 ,f(0)=0
f'(z)=2z,f'(0)=0
f^'' (z)=2z ,f^'' (0)≠0
∴order=2
Denominator: g(z)=sinz ,g(0)=0
g^' (z)=cosz ,g^' (0)≠0
∴order=1
2-1=1
Order of zero=1
When z=kπ (k≠0)
Numerator: f(z)=z^2,f(kπ)=(kπ)^2≠0
∴order=0
Denominator: g(z)=sinz ,g(kπ)=0
g^' (z)=cosz ,g^' (kπ)≠0
∴order=1
1-0=1
It is simple pole.
