Math Chapter Wise question with answer

Q01 Complex valued function 2 f(z) z, for complex z, is analytic: English · OPSC PGT 2017 Q02 The complex valued function f(z) = u(x,y) + iv(x,y), for z = x + iy, is analytic if and only if: English · OPSC PGT 2017 Q03 Let f (r cos θ+ irsin θ) = u (r, θ) + iv (r, θ). For f to be differentiable at (r, θ), Cauchy-Riemann equation stat... English · JSSC PGT 2018 Q04 If ((()) (())) ((()) u x,y iv x,y, forz 0 f z 0, forz 0 + ≠ = where ((()) 3 3 2 2 x y u x,y, x y − = + (()) 3 3 2 2... English · LT 2018 Q05 The analytic function whose real part is ex cosy is: English · NVS PGT 2022 Q06 Select the function f (z) from below that is analytic on the unit sphere z < 1. English · JSSC PGT 2018