Evaluate the complex integral $\int_{C_R}\frac{z^3}{(z-1)(z-4)^2}$ 
Let $C_R$ be the positively oriented circle with centre $3i$ and radius $R > 0$.
   Use the Cauchy Residue Theorem to evaluate the integral  $$\int_{C_R}\frac{z^3}{(z-1)(z-4)^2}$$
  Your answer should state any values of R for which the integral cannot be
  evaluated. 

Now I can find the residues of the function easily enough. They are $\frac{1}{9}$ at $z=1$ and $\frac{80}{9}$ at $z=4$. However I have no idea at what radius the points $z=1$ and $z=4$ are included in the region being integrated. Is there a way to calculate the radius at which these points need to be taken into account?

Sketch 3i , 1, 4 on a paper and use pythagorean theorem.
