Answer to Question #223820 in Chemical Engineering for Lokika

Question #223820

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


1
Expert's answer
2021-08-12T07:27:21-0400

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


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