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Let (2) denote the branch of the logarithm defined on C- [0, ∞) with 0 < Im(l(z)) < 2π. For the branch of zi+3 derived from 1(z), find (-i)i+3.

Let (2) denote the branch of the logarithm defined on C- [0, ∞) with 0 < Im(l(z)) < 2π. For the branch of zi+3 derived from 1(z), find (-i)i+3.

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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Let (2) denote the branch of the logarithm defined on C- [0, ∞) with 0 < Im(1(z)) < 2π. For the branch of zi+³ derived from 1(z), find (−i)i+³.
Transcribed Image Text:Let (2) denote the branch of the logarithm defined on C- [0, ∞) with 0 < Im(1(z)) < 2π. For the branch of zi+³ derived from 1(z), find (−i)i+³.
Expert Solution
Step 1: Writing down the given information

Let l(z) denote the branch of the logarithm defined on C−[0,∞) with 0<Im(l(z))<2π.

We need to calculate (−i)i+3 under the branch of zi+3.

We will apply the principal value of the logarithm formula given by l(z)=ln|z|+iArg(z), where Arg(z)∈(0,2π).

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