Complex integration using series expansion of analytic functions

I want to check my answer: Evaluate the following integrals: integral over gamma for (sin z)/z dz, given that gamma(t) = e^(it) , 0=click for more

Convergence of series (complex)

Find the radius of convergence of the series sum from n = 1 to infinity of n^3(z/3)^n. Does this series converge at any point on the boundary of the disk of convergence?

Analytic functions complex

Let f = u + iv be an analytic function on an open connected set G in C ( C = complex plane) where u and v are its real and imaginary parts. assume u(z) >= u(a) for some a in G and all z in G. Prove that f is constant.

Complex / Entire Function : Let f be an entire function such that |f(z)| =<10|z+1| for all |z|>100. Show that f is a linear function, f(z)= pz + q.

Let f be an entire function such that |f(z)| =<10|z+1| for all |z|>100 Show that f is a linear function, f(z)= pz + q.

Complex Cross Ratio : Evaluate cross ratio (infinity, 0, i, 1) give answer in the form a + ib where a,b in R.

Evaluate cross-ratio (infinity,0,i,1) give answer in the form a + ib where a,b in R.