1. ## Complex analysis

1)Let $f$ be an analityc function on the unit disk : $D=\left \{ \left | z \right |<1 \right \}$ and $f^2$ - polynom in domain $D$.
Is $f$ analityc function in $D$?
2)Let $f$ be an entire function and $f^2$ polynom.
Is $f$ polynom ?
2) if f is analytic but not a polynomial, $\infty$ is an essential singular point of f, so it is also an essential singular point of f^2, which contradicts the fact that f^2 is a polynomial.