An analytic function f ( z) of complex variable z = x + i y may be written asf ( z)= u ( x, y) + i v (x, y)

Q. An analytic function f ( z ) of complex variable z = x + i y may be written asf ( z)= u ( x, y) + i v (x, y) . Then, u ( x, y) and v ( x, y) must satisfy

Sol:

Analytic function f(z) = u (x, y) + iv (x, y)

If f(z) = u + iv is analytic function, then u and v must satisfy

Cauchy-Riemann (C-R) equation