Let $f:\mathbb{C}\to\mathbb{C}$ be a complex valued function of the form $f(x,y)=u(x,y)+iv(x,y)$.
Suppose that $u(x,y)=3x^2y$.
Then
$f$ cannot be holomorphic on $\mathbb{C}$ for any choice of $v$.
$f$ is holomorphic on $\mathbb{C}$ for a suitable choice of $v$.
$f$ is holomorphic on $\mathbb{C}$ for all choices of $v$.
$u$ is not differentiable.
well, I have calculated by applying CR equation, getting the option $1$ is correct? could anyone tell me just am I right?thank you.