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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

  1. $f$ cannot be holomorphic on $\mathbb{C}$ for any choice of $v$.

  2. $f$ is holomorphic on $\mathbb{C}$ for a suitable choice of $v$.

  3. $f$ is holomorphic on $\mathbb{C}$ for all choices of $v$.

  4. $u$ is not differentiable.

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well, I have calculated by applying CR equation, getting the option $1$ is correct? could anyone tell me just am I right?thank you.

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    @ZevChonoles I agree, please pardon me $f$or this time.2012-12-21

1 Answers 1

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u and v must satisfy laplace equation if f is a holomorphic function.Any v of course don't
satisfy laplace equation. hence 1 is correct. infact a form of v can be calculated by integrating the CR eequations