The Fourier Series coefficients, of a periodic signal x(t),expressed

The Fourier Series coefficients, of a periodic signal x(t),expressed as

are given by
a_–2 = – j1; a_–2 = 0.5 + j0.2; a_o = j2; a₁ = 0.5 – j0.2; a₂= 2+ j1; and a_k = 0; for |k| > 2.
Which of the following is true?

1. x(t) has finite energy because only finitely many coefficients are non-zero
2. x(t) has zero average value because it is periodic
3. The imaginary part of x(t) is constant
4. The real part of x(t) x(t) is even

So imaginary part of x(t) is constant = 2
x(t) has finite energy because only finite coefficients are zero.