Answer to Question #223820 in Chemical Engineering for Lokika

Question

Which of the following function is NOITan entire function. A. Ln(z) B.  e^{z^{2}} C cosz  D.  z^{3}+5z

Answer 1

Part A

$\ln(z) = \ln(ze^{i \theta})\\$

This is an entire function

Part B

$e^{z^{2}} = \sum_{n=0}^{\infin}(\frac{z^n}{n!})^2\\$

This is an entire function

Part C

$cos(z)= \frac{e^{i z}+e^{-i z}}{2}\\$

This is an entire function.

Part D

$z^3+5z = \frac{e^{i z}+e^{-i z}}{2}= \frac{e^{i z}+e^{-i z}}{-2i}\\\\$

This is NOT an entire function