Question

1. a. i. Discuss whether or not the following transformation provides conformal mapping throughout the entire z-plane w = z + 4/z ii. Find the Bilinear Transformation that map z = 0, -i, -1 onto w = i, 1, 0. b. Evaluate i. ?_C (12z² - 4i) dz along the straight line joining the points (1, 1) and (2, 3). ii. ?_C (z - z²) dz where C is the upper half of the circle |z - 2| = 3.

          1. a. i. Discuss whether or not the following transformation provides conformal mapping throughout the entire z-plane
w = z + 4/z
ii. Find the Bilinear Transformation that map z = 0, -i, -1 onto w = i, 1, 0.
b. Evaluate
i. ?_C (12z² - 4i) dz along the straight line joining the points (1, 1) and (2, 3).
ii. ?_C (z - z²) dz where C is the upper half of the circle |z - 2| = 3.

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1. a. i. Discuss whether or not the following transformation provides conformal mapping throughout the entire z-plane
w = z + 4/z
ii. Find the Bilinear Transformation that map z = 0, -i, -1 onto w = i, 1, 0.
b. Evaluate
i. ?C (12z² - 4i) dz along the straight line joining the points (1, 1) and (2, 3).
ii. ?C (z - z²) dz where C is the upper half of the circle |z - 2| = 3.

Added by Jamie K.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Sri K

09/02/2023

Step 1

a. i. To determine if the transformation 4w = z + 5 provides conformal mapping throughout the entire z-plane, we need to check if it preserves angles and if it has a non-zero derivative. The transformation can be written as w = (z + 5)/4. Let's find its Show more…

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1. a. i. Discuss whether or not the following transformation provides conformal mapping throughout the entire z-plane w = z + 4/z ii. Find the Bilinear Transformation that map z = 0, -i, -1 onto w = i, 1, 0. b. Evaluate i. ∫_C (12z² - 4i) dz along the straight line joining the points (1, 1) and (2, 3). ii. ∫_C (z - z²) dz where C is the upper half of the circle |z - 2| = 3.

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