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Complex numbers › Complex analysis › Contour integrals

Argument principle on a doubly traversed circle

University · ●●○○○ 20 pts

Let f(z)=z3ez2f(z)=z^3e^{z^2} for z∈Cz\in\mathbb{C}, and let Γ\Gamma be the circle z=eiθz=e^{i\theta}, where 0≤θ≤4π0\leq\theta\leq4\pi, so the contour goes around the unit circle twice counterclockwise. Find 12πi∮Γf′(z)f(z) dz\frac{1}{2\pi i}\oint_{\Gamma} \frac{f'(z)}{f(z)}\,dz.

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contour integration