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I don't know where to begin with this question. Can anyone help me?

Let be a semicircular path with centre at and with radius of 1 in the left half plane, that is, it is the straight line from 2 to 0 followed by left half a circle from 0 back to 2i.

enter image description here

Evaluate $$\oint_C \bar z dz$$

Kat L
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1 Answers1

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hint

Along the vertical line, we have

$$z=it$$ with $$0\le t\le 2, \bar{z}=-it, \;\; dz=idt$$

along the half-circle

$$z-i=e^{it}$$

with $$\frac{\pi}{2}\le t\le \frac{3\pi}{2}$$

hamam_Abdallah
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