# 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 and hmmm16

#### 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,

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