- #1
Mattbringssoda
- 16
- 1
Homework Statement
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Find and classify all singularities for (e-z) / [(z3) ((z2) + 1)]
Homework Equations
The Attempt at a Solution
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This is my first attempt at these questions and have only been given very basic examples, but here's my best go:
I see we have singularities at 0 and i.
The 0 corresponds with z3, so upon inspection it's a third order pole.
To determine the order for the i singularity, I multiply the function by (z - i) and use L'Hospital's rule
Lim (z -> i ) of [ (z-i) (e-z) ] / [ (z3) ((z2) + 1) ]
= Lim (z -> i) of [ (z-i) (-e-z) + (e-z) ] / [ (5z4) + 3z2 ]
= (e^-i) / 2
Which is a finite number, and since I used the first order term (1-i), this is indeed a first order pole, according to what I've been taught.
I'm worried that I'm misunderstanding how to use L'Hospital here and was hoping I could get a second set of eyes from someone familiar with these problems.
Thanks!