Project ForgeEngineering Mathematics
Calculus
GATE 2019
Medium
An analytic function f(z) of complex variable z=x+iy may be written as f(z)=u(x,y)+iv(x,y). Then, u(x,y) and v(x,y) must satisfy
- A∂u/∂x=∂v/∂y and ∂u/∂y=∂v/∂x
- ∂u/∂x=∂v/∂y and ∂u/∂y=−∂v/∂x
- C∂u/∂x=−∂v/∂y and ∂u/∂y=∂v/∂x
- D∂u/∂x=−∂v/∂y and ∂u/∂y=−∂v/∂x
Explanation
These are exactly the Cauchy-Riemann equations, the necessary condition for f(z)=u+iv to be analytic: u_x=v_y and u_y=−v_x.
Source: GATE ME 2019 Session 2 (Set 3) (2019)
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