Exercise · ZW-ISOLATED-SINGULARITY-003 · ★☆☆ Basic
What kind of singularity does \(\frac1{z^2+1}\) have at \(z=i\)?
Choose one option.
Show answer
- B. Simple pole
Explanation
Factor it as \(\frac1{(z-i)(z+i)}\): the factor \(z-i\) appears to the first power, and \(\frac1{z+i}\) is holomorphic and nonzero at \(i\). It is a simple pole.
Review the concept: Isolated singularity
An isolated singularity of a function \(f\) is a point \(z_0\) where \(f\) is not holomorphic but is holomorphic on a punctured disc \(0<|z-z_0|<r\) around it.
More practice problems: isolated singularity
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