evaluate a complex integral

hmmm16

Member
Is my solution to the following problem correct?

Evaluate $$\int_\gamma \frac{z^3}{z-3} dz$$ where $\gamma$ is the circle of radius 4 centered at the origin.

Solution

Form the cauchy integral formula we have that:

$$f(3)=\frac{1}{2\pi i} \int_\gamma \frac{z^3}{z-3}dz$$ and so $$\int_\gamma \frac{z^3}{z-3} dz=54\pi i$$

Thanks very much for any help

dwsmith

Well-known member
Is my solution to the following problem correct?

Evaluate $$\int_\gamma \frac{z^3}{z-3} dz$$ where $\gamma$ is the circle of radius 4 centered at the origin.

Solution

Form the cauchy integral formula we have that:

$$f(3)=\frac{1}{2\pi i} \int_\gamma \frac{z^3}{z-3}dz$$ and so $$\int_\gamma \frac{z^3}{z-3} dz=54\pi i$$

Thanks very much for any help
Looks fine.

Sudharaka

Well-known member
MHB Math Helper
Is my solution to the following problem correct?

Evaluate $$\int_\gamma \frac{z^3}{z-3} dz$$ where $\gamma$ is the circle of radius 4 centered at the origin.

Solution

Form the cauchy integral formula we have that:

$$f(3)=\frac{1}{2\pi i} \int_\gamma \frac{z^3}{z-3}dz$$ and so $$\int_\gamma \frac{z^3}{z-3} dz=54\pi i$$

Thanks very much for any help
Hi hmmm16,