Grade upto college level Trigonometry
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 Answer
bharat bajaj
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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