x[n] is a real periodic signal with period N and complex Fourier series coefficients...

x[n] is a real periodic signal with period N and complex Fourier series coefficients be denoted by

where are both real.

(a) Show that ?

(b) Suppose that N is even. Show that is real.

(c) Show that x[n] can also be expressed as a trigonometric Fourier series of the form