Evaluate $\int(\overline z + 2z)dz$ along the circle $x^2+y^2 = 1.$

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written 7.9 years ago by

teamques10 ★ 65k

modified 17 months ago by

sagarkolekar ★ 11k

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written 7.9 years ago by

teamques10 ★ 65k

• modified 7.9 years ago

$x^2+ y^2 = 1$ is a circle with center $(0,0)$ and radius $= 1$ $$\text { put }z=reiθ = 1 eiθ$$

$$∴dz = eiθ . idθ $$

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and, $= e^{-iθ} $

$$∴ = . ie^{iθ}dθ$$

$$= i . dθ$$

$$= i [1θ +]_0^{2π}$$

$$= i ]$$

Now, $$= \cos 4π …

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