Evaluate the closed contour integral

**lpd** · November 21st 2010, 05:57 PM

Consider a piecewise smooth contour $\Gamma$ which is a triangle with vertices at $z = 0, 1 + i, i$ . Evaluate the closed contour integral,

$$\int_\Gamma\bar{z}^3 dz$

around the triangle $\Gamma$ by suitably parametrizing the segments of the piecewise smooth contour $\Gamma$ .

Why doesn’t Cauchy’s theorem apply to this integral?

**tonio** · November 21st 2010, 06:14 PM

Originally Posted by lpd

Consider a piecewise smooth contour $\Gamma$ which is a triangle with vertices at $z = 0, 1 + i, i$ . Evaluate the closed contour integral,

$$\int_\Gamma\bar{z}^3 dz$

around the triangle $\Gamma$ by suitably parametrizing the segments of the piecewise smooth contour $\Gamma$ .

Why doesn’t Cauchy’s theorem apply to this integral?

Because $f(z)=\bar{z}^3$ isn't analytic...

Tonio

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