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1. (a) How are the functions e², √sin z, log z defined? Which functions here are multiple- valued? (b) Prove or disprove: Im z = Im z, log(z) = log z, where log z denotes the set of all values. (c) Calculate logz and √z for z = Justify your answer. 1+√/3i 1-i

1. (a) How are the functions e², √sin z, log z defined? Which functions here are multiple- valued? (b) Prove or disprove: Im z = Im z, log(z) = log z, where log z denotes the set of all values. (c) Calculate logz and √z for z = Justify your answer. 1+√/3i 1-i

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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1. (a) How are the functions e*. Vsin z, log z defined? Which functions here are multiple- valued? (b) Prove or disprove: Im z Imz, log(z) = log z, where log z denotes the set of all values. (c) Calculate log z and √z for z = Justify your answer. 1+√³i 1-i
Transcribed Image Text:1. (a) How are the functions e*. Vsin z, log z defined? Which functions here are multiple- valued? (b) Prove or disprove: Im z Imz, log(z) = log z, where log z denotes the set of all values. (c) Calculate log z and √z for z = Justify your answer. 1+√³i 1-i
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