Use Euler's relation to represent the signal x3[n]= cos(2πk0n/N) as a sum of two compl...

Use Euler's relation to represent the signal x3[n]= cos(2πk0n/N) as a sum of two complex exponentials. Use the fact that the DFT, like its cousins the z-transform and the DTFT, is a linear operation to show that

or equivalently