GATE EC ||MATHEMATICS || NUMERICAL METHOD || PYQs(2000-2025)

Which one of the following functions is analytic over the entire complex plane?

Consider the complex valued function f(z) = 2z³ + b|z|³ where z is a complex variable. The value of b for which the function f(z) is analytic is ___

For f(z) = sin(z) / z², the residue of the pole at z = 0 is ___.

The residues of a function f(z) = 1 / (z − 4)(z + 1)³ are ___