![An analytic function f ( z) of complex variable z = x + i y may be written asf ( z)= u ( x, y) + i v (x, y)](https://www.gkseries.com/blog/wp-content/uploads/2023/09/An-analytic-function-f-z-of-complex-variable-z-x-i-y-may-be-written-asf-z-u-x-y-i-v-x-y-1.jpg)
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
![](https://www.gkseries.com/blog/wp-content/uploads/2023/09/image-1.png)