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7. Let f(z) be the principal branch of z-i. (a) Write f(z) explicitly and calculate f(i). (b) For Z₁, Z2 #0, show that f(Z1)f(Z2) f(Z122) = 1, е-2, or e²π You may use the following fact without proof: Arg(21) + Arg(22) - Arg(2122) = {0,2π, -2π}.

7. Let f(z) be the principal branch of z-i. (a) Write f(z) explicitly and calculate f(i). (b) For Z₁, Z2 #0, show that f(Z1)f(Z2) f(Z122) = 1, е-2, or e²π You may use the following fact without proof: Arg(21) + Arg(22) - Arg(2122) = {0,2π, -2π}.

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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7. Let f(z) be the principal branch of z-i. (a) Write f(z) explicitly and calculate f(i). (b) For z₁,z2 #0, show that f(z1)f(Z2) f(Z1Z2) = 1, е-2π, or e² You may use the following fact without proof: Arg(z1) + Arg(22) - Arg(2₁22) = {0,2π, -2π}.
Transcribed Image Text:7. Let f(z) be the principal branch of z-i. (a) Write f(z) explicitly and calculate f(i). (b) For z₁,z2 #0, show that f(z1)f(Z2) f(Z1Z2) = 1, е-2π, or e² You may use the following fact without proof: Arg(z1) + Arg(22) - Arg(2₁22) = {0,2π, -2π}.
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