Question

The complex function $e^{-\left(\frac{2}{z-1}\right)}$ has:

• A. a simple pole at $z = 1$
• B. an essential singularity at $z = 1$
• C. a residue equal to $-2$ at $z = 1$
• D. a branch point at $z = 1$

Answer 1

Answer: (B), (C)

an essential singularity at $z = 1$

Answer 2

The correct options are (B) :an essential singularity at $z = 1$ ,(C):a residue equal to $-2$ at $z = 1$