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## Homework Statement

As in thread title.

## Homework Equations

Residue Theorem.

## The Attempt at a Solution

I just need help figuring out the circle C I'll be using. Suggestions?

- Thread starter Jamin2112
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As in thread title.

Residue Theorem.

I just need help figuring out the circle C I'll be using. Suggestions?

- #2

vela

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What does the presence of z^{2/3} tell you?

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Other than that there's a pole at z=0?What does the presence of z^{2/3}tell you?

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vela

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Yes, other than that. In particular, what's the effect of the fractional power?

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Change the distance between z and the origin from r to rYes, other than that. In particular, what's the effect of the fractional power?

Change the angle between z and the x-axis from ø to 2ø/3

- #6

vela

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Right. Do you know what a branch point and a branch cut are?

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Yeah, I somehow need a loop that avoid z=-1 and z=0. Right?Right. Do you know what a branch point and a branch cut are?

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vela

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So I'd take R>1 and make a half circle of radius R in the upper half of the plane. Then I'd make two little half circles that jump over z=-1 and z=0. Then I'd look at ∫

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vela

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Also, rewrite the integrand as

$$\frac{z^{1/3}}{z(z+1)}$$to make it clear how to calculate the residue at z=0.

- #11

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So in my case the path should resemble a backwards Pacman?

Also, rewrite the integrand as

$$\frac{z^{1/3}}{z(z+1)}$$to make it clear how to calculate the residue at z=0.

- #12

vela

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Doesn't the answer to that question depend on which way Pacman is moving?

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I forgot that PacMan is in perpetual motion.Doesn't the answer to that question depend on which way Pacman is moving?

But yeah, how am I gonna do this? I need C to be formed from a series of paths, each of which will have a line integral that approaches a real value after I take some limit.

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vela

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How would that work? I want ∫f(x)dx (integrated on [0, R]) to be one of the four line integrals.

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