CSIR NET Mathematics 2022| Complex Analysis (17 NOVEMBER)

For any complex valued function f let D_f denote the set on which the function f satisfies Cauchy-Riemann equations. Identify the functions for which D_f is equal to ℂ .

Let C be the circular contour taken counterclockwise. The line integer  is equal to

Given a real number a > 0, consider the triangle  with vertices 0, a, a + ia. If  is given the counter clockwise orientation, then the contour integral  (with Re(z) denoting the real part of z) is equal to

Which of the following function has removable singularity at z =0

Let C denote the positively oriented boundary of the square whose sides lie along the line Let then