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
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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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