Part BCSIR NET June 2024parametrisation-winds-twice

Parametrisation winds twice

Consider the contour $γ$ given by $γ (θ) = e^{(} 2 i θ)$ for $θ \in [0, π /2]; γ (θ) = 1 + 2 e^{(} 2 i θ)$ for $θ \in [π /2, 3 π /2]; γ (θ) = e^{(} 2 i θ)$ for $θ \in [3 π /2, 2 π]$ . Then what is the value of $\int_{γ}$ dz / (z(z − 2))?

A.0
B. $π i$
C. $- π i$ ✓
D. $2 π i$

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

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Parametrisation winds twice

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