# Show that $f$ is a polynomial regarding a given question

Since $$f$$ is entire it satisfies Cauchy Riemann so $$u_x=v_y \& 0=u_y=v_x$$

But how does that show $$f$$ is a polynomial?

$$u_x$$ and $$v_y$$ are functions only of $$x$$ and of $$y$$ respectively, so the only way they’re equal is if they are constants.
• @ErockBrox ??? $0$ is certainly a polynomial. – David C. Ullrich Jan 20 at 18:42