Is the following statement valid according to Euler's formula? Cos(2npi) = (-1)^2n

QUESTION POSTED AT 29/05/2020 - 12:55 AM

Answered by admin AT 29/05/2020 - 12:55 AM

Provided that n is an integer, the statement is true.

(-1)^{2n}=((-1)^2)^n=(1)^n=1

Meanwhile, Euler's formula gives us

(-1)^{2n}=(e^{i\pi})^{2n}=e^{i(2n\pi)}=\cos(2n\pi)+i\sin(2n\pi)

and we know that \sin2n\pi=0 for all integers n, while \cos2n\pi=1.
Post your answer

Related questions

Solve the formula d=st for s

QUESTION POSTED AT 01/06/2020 - 03:24 PM