Hi Any help with this question would be greatly appreciated - I just cant get my head around the squared term in the denominator:

(a) Evaluate the integral:

Int (e^zpi)/((z+i)(z-3i)^2) when

(i) C= {z:|z|=2}

(ii) C = {z:|z-1|=1}

(iii) C = {z:|z-2i|=2}

(b) Use liouvilles theorem to show that there is at least one value z subset C for which |sinz|>2007

(c) Show that if f is an entire function that satisfies |2007i+f(z)|>2007 then f is constant

(d) Deduce from the result in (b) that if f is an entire function that satisfies Im(f(z))>0 for all z subset c, then f is constant

Many thanks