Let f(z) = ((z – 3i)² + 9)ez-si The Laurent series representation of f(z) in the domain 0 < |z – 3i| < o. 1 1 a) (z-3)2 + (z- 3i) + Σo( +): \(n+2)! n!) (z-3i)n 1 1 b) 2(z – 3i) + En=o} n! (z-3i)n 1 c) 9 + 9(z – 3i) + E%=2 (n-2)! u(1£ – 2) (* +

Let f(z) = ((z – 3i)² + 9)ez-si The Laurent series representation of f(z) in the domain 0 < |z – 3i| < o. 1 1 a) (z-3)2 + (z- 3i) + Σo( +): \(n+2)! n!) (z-3i)n 1 1 b) 2(z – 3i) + En=o} n! (z-3i)n 1 c) 9 + 9(z – 3i) + E%=2 (n-2)! u(1£ – 2) (* +

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

Complex number Please help with details explanation

Let f(z) = ((z – 3i)² + 9)ez-i
The Laurent series representation of f(z) in the domain 0 < |z – 3i| < ∞.
a) (z – 3i)? + (z – 3i) + En=o (42t )-31)
1
n%3D0\(n+2)!
n!/
1
n! (z-3i)n
1
b) 2(z – 3i) + En=o
c) 9+ 9(z – 3i) + En=2
\(n-2)!

Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.

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