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 have2 + 3i| ≤7and |z + 1| ≥ 1.(Hint: use the triangle and reverse triangle inequalities respectively).(b) Use part (a) to find an upper estimate for the integralz + 3i√ ₁ ( Z + 1)²dz.

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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.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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