Im-C-0-1-2-z-dz-pi-2-

Question Number 136682 by snipers237 last updated on 24/Mar/21

I m (\int_{C^{+} (0, \frac{1}{2})} \bar{z d z}) = \frac{π}{2}

Answered by Olaf last updated on 24/Mar/21

Ω = Im \int_{C^{+} (0, \frac{1}{2})} \bar{z d z}

Ω = Im \int_{0}^{2 π} \frac{1}{2} e^{- i θ} d (\frac{1}{2} e^{i θ})

Ω = \frac{1}{4} Im \int_{0}^{2 π} i d θ

Ω = \frac{1}{4} Im (2 π i) = \frac{2 π}{4} = \frac{π}{2}

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