Question

A function $f$ of the complex variable $z=x+iy$, is given as $f(x,y)=u(x,y)+iv(x,y),whereu(x,y)=2kxy$ and $v(x,y)=x^2-y^2$. The value of $k$, for which the function is analytic, is

• A. -1

Answer 1

The correct option is A -1
$u(x,y)=2kxy$ and $v(x,y)=x^2-y^2$
Now, $\frac{\partial u}{\partial x}=\frac{\partial v}{\partial y}and\frac{\partial u}{\partial y}=-\frac{\partial v}{\partial x}$
$\Rightarrow 2ky=-2y$ and $2kx=-2x$
$\Rightarrow k=-1$ and $k=-1$