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Let I be the simple, closed, anticlockwise contour whose points lie on the circle {z € C : |z + 4| = 2}. (a) Show that for every z E I we have |z+3i| ≤ 7 and |z + 1| ≥ 1. (Hint: use the triangle and reverse triangle inequalities respectively). (b) Use part (a) to find an upper estimate for the integral z + 3i SEZ (z + 1)² dz.

Let I be the simple, closed, anticlockwise contour whose points lie on the circle {z € C : |z + 4| = 2}. (a) Show that for every z E I we have |z+3i| ≤ 7 and |z + 1| ≥ 1. (Hint: use the triangle and reverse triangle inequalities respectively). (b) Use part (a) to find an upper estimate for the integral z + 3i SEZ (z + 1)² dz.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let I be the simple, closed, anticlockwise contour whose points lie on the circle {z € C : |z + 4| = 2}. (a) Show that for every z E I we have 2 + 3i| ≤7 and |z + 1| ≥ 1. (Hint: use the triangle and reverse triangle inequalities respectively). (b) Use part (a) to find an upper estimate for the integral z + 3i √ ₁ ( Z + 1)² dz.
Transcribed Image Text:Let I be the simple, closed, anticlockwise contour whose points lie on the circle {z € C : |z + 4| = 2}. (a) Show that for every z E I we have 2 + 3i| ≤7 and |z + 1| ≥ 1. (Hint: use the triangle and reverse triangle inequalities respectively). (b) Use part (a) to find an upper estimate for the integral z + 3i √ ₁ ( Z + 1)² dz.
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