show that e^z=1 if and only if Z is an integral multipal of 2(pi)(iota)?

Question

bharat bajaj · Answer

Say z = 2(pi)i * n where n can be anything.
e^(2pi*n*i) = cos(2pi*n) + i sin(2pi*n)

Hence this can only be 1 when imaginory part of this equation is 0. Hence,
sin(2pi*n) = 0
This is valid only when n is an integer.
Hence Proved.

Thanks & Regards
Bharat Bajaj
askIITians Faculty
Qualification.
IIT Delhi

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

show that e^z=1 if and only if Z is an integral multipal of 2(pi)(iota)?

show that e^z=1 if and only if Z is an integral multipal of 2(pi)(iota)?

1 Answers

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

Other Related Questions on Algebra

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship