If f(z) = (x2 + ay2) + ibxy is a complex analytic function

Home » Engineering Mathematics » Engineering Mathematics Miscellaneous » Question

If f(z) = (x² + ay²) + ibxy is a complex analytic function of z = x + iy, where i = √- 1, then

1. a = –1, b = –1
2. a= –1, b = 2
3. a = 1, b = 2
4. a = 2, b = 2

Correct Option: B

For analytic function,
f (2) = (x² + a y²) + ibxy
u + iv = (x² + ay²) + i (bxy)
u = x² + ay²; v = bxy
u_x = 2x; u_y = 2 ay
V_x = b_y; V_y = bx
u_x = V_y; u_y = –V_x
2 x = bx; 2ay = –by
By solving, we get
a = –1 b = 2