12. Determine the range of f(z) = z² for 1 < x <2 and 1 < y < 3. Map the four lines that are boundaries for the domain in the z-plane into the w-plane. 13. Determine the range of f(z) = iz +2 for 0 < x < ∞ and 0 < y < ∞o. Map the lines that are boundaries for the domain in the z-plane into the w-plane. 14. Show that the two families of curves, u(x, y) = uo and v(x, y) = vo, associated with f(z) = iz are orthogonal.
12. Determine the range of f(z) = z² for 1 < x <2 and 1 < y < 3. Map the four lines that are boundaries for the domain in the z-plane into the w-plane. 13. Determine the range of f(z) = iz +2 for 0 < x < ∞ and 0 < y < ∞o. Map the lines that are boundaries for the domain in the z-plane into the w-plane. 14. Show that the two families of curves, u(x, y) = uo and v(x, y) = vo, associated with f(z) = iz are orthogonal.
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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Transcribed Image Text:12. Determine the range of f(z) = z² for 1 < x <2 and 1 < y < 3. Map the four lines that are boundaries for the
domain in the z-plane into the w-plane.
13. Determine the range of f(z) = iz +2 for 0 < x < ∞ and 0 < y < ∞o. Map the lines that are boundaries for
the domain in the z-plane into the w-plane.
14. Show that the two families of curves, u(x, y) = uo and v(x, y) = vo, associated with f(z) = iz are orthogonal.
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