Complex integral 1/(z^21)

1. How do you find the complex integral?
2. What is the integral of 1 z?
3. What is the integration of E to the power Z?
4. How do you use Cauchy integral formula?

How do you find the complex integral?

Contour integral

Consider a contour C parametrized by z(t)=x(t)+iy(t) for a≤t≤b. We define the integral of the complex function along C to be the complex number ∫Cf(z)dz=∫baf(z(t))z′(t)dt.

What is the integral of 1 z?

The only singularity of the function f(z) = 1/z is at z=0 and so the (line) integral of 1/z around any closed contour not enclosing z=0, is 0.

What is the integration of E to the power Z?

The integral of ez with respect to z is ez .

How do you use Cauchy integral formula?

Statement: If f(z) is an analytic function in a simply-connected region R, then ∫_c f(z) dz = 0 for every closed contour c contained in R. If f(z) is an analytic function and its derivative f'(z) is continuous at all points within and on a simple closed curve C, then ∫_c f(z) dz = 0.