I'm studying for a test.(adsbygoogle = window.adsbygoogle || []).push({});

The question is:

Let A be the straight line segment from -3-4i to 4+3i. Let B be the arc of the circle |z| = 5 going anti-clockwise from -3-4i to 4+3i. Let C be the arc of the circle |z| = 5 going anti-clockwise from -3-i to 4+3i. Define:

I_{A}= [tex]\int_A[/tex] 1/z dz

I_{B}= [tex]\int_B[/tex] 1/z dz

I_{C}= [tex]\int_C[/tex] 1/z dz

How do I calculate I_{A}, I_{B}, I_{C}? I know to write I_{A}as an integral by parameterizing A, but how do I parameterize A, I know if I can find I_{A}then the other two are easy. Could I let z = e^{it}so dz = ie^{it}dt. I can't seem to get the limits integration.

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# Line integral

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