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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)?

Grade:11

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
8 years ago
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

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