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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
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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(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
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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