The complex function \( e^{-\left(\frac{2}{z-1}\right)} \) has:
- a simple pole at \( z = 1 \)
- an essential singularity at \( z = 1 \)
- a residue equal to \( -2 \) at \( z = 1 \)
- a branch point at \( z = 1 \)
The Correct Option is B, C
Solution and Explanation
Top Questions on Complex Functions
- Find the residue of the function \[ f(z) = \frac{1}{z^2 + 1} \] at the pole $z = i$.
- TS PGECET - 2025
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Let \( \Omega \) be a non-empty open connected subset of \( \mathbb{C} \) and \( f: \Omega \to \mathbb{C} \) be a non-constant function. Let the functions \( f^2: \Omega \to \mathbb{C} \) and \( f^3: \Omega \to \mathbb{C} \) be defined by \[ f^2(z) = (f(z))^2 \quad {and} \quad f^3(z) = (f(z))^3, \quad z \in \Omega. \]
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