Question

The Fourier series expansion of a real periodic signal with fundamental frequency $f_0$ is given by
$g_p\left(t\right)={\sum }_{n=-\infty }^{\infty }{c}_n{e}^{j2\pi n{f}_{0}t}$ it is given that $c_3=3+j5.$ Then $C_{-3}$ is

• A.
  $-3-j5$
• B.
  $5+j3$
• C.
  $3-j5$
• D.
  $-5+j3$

Answer 1

The correct option is C

$3-j5$
$C_{-k}=C_k^{\ast }$

$C_3=3+j5$

$C_{-3}=C_k^{\ast }=3-j5$