Problem $8(3$ points$).$ Find the Taylor series expansion $of$ the function $at$ the indicated

point $z_0.$ Determine the radius $of$ convergence.

$(a)$

$f(z)=\frac{2i}{3-iz},z_0=-1$

$(b)$

$f(z)=\frac{z^2+1}{z-1},z_0=0$

$(c)$

$f(z)=z{e}^{3z^2},z_0=0$