5) Compute ln(z) for the following complex numbers under the given branch cut. (a) In ( 1/1 + ²√³) ³) with branch cut given by the curve y(x) : [0, ∞) → R² y(x) = [[x, x]¹ [x, 2] ¹ 0≤x≤2 x ≥ 2. and ln(1) = 0 (b) ln (√3+ i) with branch cut given by the curve y(a): [0, ∞) → R², y(x) = [x, √√3x²]T with ln(1) = 0
5) Compute ln(z) for the following complex numbers under the given branch cut. (a) In ( 1/1 + ²√³) ³) with branch cut given by the curve y(x) : [0, ∞) → R² y(x) = [[x, x]¹ [x, 2] ¹ 0≤x≤2 x ≥ 2. and ln(1) = 0 (b) ln (√3+ i) with branch cut given by the curve y(a): [0, ∞) → R², y(x) = [x, √√3x²]T with ln(1) = 0
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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Question
![(a) In
s) Compute In(z) for the following complex numbers under the given branch cut.
+ with branch cut given by the curve y(x) : [0, ∞) → R²
i√3
2
y(x) =
=
[[x, x]¹ 0≤x≤2
[x, 2]T x ≥ 2.
and ln(1) = 0
(b) ln (√√3+i) with branch cut given by the curve y(x): [0, ∞) → R², y(x) = [x, √√3x²]T
with ln(1) = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F27d05195-d4e5-49f1-8dc4-61bbc8dbf8a7%2F31d23526-8400-4e55-959c-b288985bba25%2Fy4kvu9o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) In
s) Compute In(z) for the following complex numbers under the given branch cut.
+ with branch cut given by the curve y(x) : [0, ∞) → R²
i√3
2
y(x) =
=
[[x, x]¹ 0≤x≤2
[x, 2]T x ≥ 2.
and ln(1) = 0
(b) ln (√√3+i) with branch cut given by the curve y(x): [0, ∞) → R², y(x) = [x, √√3x²]T
with ln(1) = 0
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