- #1

squenshl

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I'm studying for a test.

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

I

I

How do I calculate I

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 dzI

_{B}= [tex]\int_B[/tex] 1/z dzI

_{C}= [tex]\int_C[/tex] 1/z dzHow 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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