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1. Consider the function w(z) - i2² +1. (a) Write the function w(2) in the form 4 w(r +iy)=u(x, y) +iv(z,y) C 4 where x, y, u(x, y) and v(x, y) are real-valued. In other words, find u(x, y) and v(x, y). (b) Describe/sketch the image of the curves (i.e. the shape, intercepts on the principal axes, ...) i. r= 1, and ii. y = 0 under the transformation w (i.e. in the u-v plane).

1. Consider the function w(z) - i2² +1. (a) Write the function w(2) in the form 4 w(r +iy)=u(x, y) +iv(z,y) C 4 where x, y, u(x, y) and v(x, y) are real-valued. In other words, find u(x, y) and v(x, y). (b) Describe/sketch the image of the curves (i.e. the shape, intercepts on the principal axes, ...) i. r= 1, and ii. y = 0 under the transformation w (i.e. in the u-v plane).

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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help with b March 2019 1. Consider the function w(z)= iz² +1. (a) Write the function w(z) in the form 4 w(r+iy)= u(x, y) + iv(x, y) 4 where x, y, u(x, y) and v(x, y) are real-valued. In other words, find u(x, y) and v(x, y). (b) Describe/sketch the image of the curves (i.e. the shape, intercepts on the principal axes, ...) i. r= 1, and ii. y = 0 under the transformation w (i.e. in the u-v plane).
Transcribed Image Text:help with b March 2019 1. Consider the function w(z)= iz² +1. (a) Write the function w(z) in the form 4 w(r+iy)= u(x, y) + iv(x, y) 4 where x, y, u(x, y) and v(x, y) are real-valued. In other words, find u(x, y) and v(x, y). (b) Describe/sketch the image of the curves (i.e. the shape, intercepts on the principal axes, ...) i. r= 1, and ii. y = 0 under the transformation w (i.e. in the u-v plane).
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