The value of , where C is the boundary of |z - i| = 1, is

Concept:

Cauchy's theorem:

If f(z) is an analytic function and f'(z) is continuous at each point within and on a closed curve C, or if the simple closed curve does not contain any singular point of f(z) then,

Given,

The integral is  where C is |z -i| = 1

Now, for point singularity consider Z² + 6 = 0

Therefore point of singularity is a = ± √6i

For |z -i| = 1 we have,

radius r = 1,  centre c = (0,1),

a = ± √6i is out of circle,

By Cauchy's Integral Formula We have,

 = 0