-
A function f of the complex variable z = x + iy, is given as f(x, y) = u(x, y) + iv(x, y), where u(x, y) = 2 kxy and v(x, y) = x² – y². The value of k, for which the function is analytic, is_____
-
- - 1
- - 2
- - 3
- - 4
Correct Option: A
Given that f (z) = u + i v is analytic
u (x,y) = 2 kxy v = x² – y²
ux = 2ky vy = – 2y
ux = vy
k = –1
uy = 2kx vx = 2x
uy = –vx
2kx = –2x
k = –1
