Question

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

Answer 1

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`.