cmi-entrance 2014 Q16

cmi-entrance · India · pgmath 10 marks Not Maths
Let $f : \mathbb{C} \rightarrow \mathbb{C}$ be an entire function.
(A) Construct a sequence $\{z_n\}$ in $\mathbb{C}$ such that $|z_n| \rightarrow \infty$ and $e^{z_n} \rightarrow 1$.
(B) Show that the function $g(z) = f\left(e^z\right)$ is not a polynomial.
Let $f : \mathbb{C} \rightarrow \mathbb{C}$ be an entire function.\\
(A) Construct a sequence $\{z_n\}$ in $\mathbb{C}$ such that $|z_n| \rightarrow \infty$ and $e^{z_n} \rightarrow 1$.\\
(B) Show that the function $g(z) = f\left(e^z\right)$ is not a polynomial.