For the second-order linear differential equation with complex conjugate roots r = + i and s = i, show that y(t) =

For the second-order linear differential equation with complex conjugate roots r = α + βi and s = α − βi, show that y(t) = c1ert + c2est is equivalent to y(t) = c1eαi cos(βt) + c2eαi sin(βt)

by using Euler’s identity that for the complex number iβ

eiβ = cos β + isin β