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evaluate a complex integral

hmmm16

Member
Feb 25, 2012
31
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
Feb 1, 2012
1,673
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
Feb 5, 2012
1,621
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,

Your answer is correct.