Solveeit Logo
Login

Question

Engineering Mathematics Question on Complex Functions

In a complex function
f(x,y)=u(x,y)+iv(x,y),f(x, y) = u(x, y) + i v(x, y),
ii is the imaginary unit, and x,y,u(x,y)x, y, u(x, y) and v(x,y)v(x, y) are real.
If f(x,y)f(x, y) is analytic then which of the following equations is/are TRUE?

A

∂2u∂x2+∂2u∂y2=0\frac {∂^2u}{∂x^2}+\frac {∂^2u}{∂y^2}=0

B

∂2v∂x2+∂2v∂y2=0\frac {∂^2v}{∂x^2}+\frac {∂^2v}{∂y^2}=0

C

∂2u∂x2+∂2v∂y2=0\frac {∂^2u}{∂x^2}+\frac {∂^2v}{∂y^2}=0

D

(∂u∂x)(∂v∂x)+(∂u∂y)(∂v∂y)=0(\frac {∂u}{∂x})(\frac {∂v}{∂x})+(\frac {∂u}{∂y})(\frac {∂v}{∂y})=0

Answer

∂2u∂x2+∂2u∂y2=0\frac {∂^2u}{∂x^2}+\frac {∂^2u}{∂y^2}=0

Explanation

Solution

The correct options are (A), (B) and (D).