- #1
squenshl
- 479
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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:
IA = [tex]\int_A[/tex] 1/z dz
IB = [tex]\int_B[/tex] 1/z dz
IC = [tex]\int_C[/tex] 1/z dz
How do I calculate IA, IB, IC? I know to write IA as an integral by parameterizing A, but how do I parameterize A, I know if I can find IA then the other two are easy. Could I let z = eit so dz = ieit dt. I can't seem to get the limits integration.
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:
IA = [tex]\int_A[/tex] 1/z dz
IB = [tex]\int_B[/tex] 1/z dz
IC = [tex]\int_C[/tex] 1/z dz
How do I calculate IA, IB, IC? I know to write IA as an integral by parameterizing A, but how do I parameterize A, I know if I can find IA then the other two are easy. Could I let z = eit so dz = ieit dt. I can't seem to get the limits integration.
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