For a real signal, $x(n)$ =$x^*(n)$ . Taking Z-transform on both sides,
$X(z)$=$X^*(z^*)$ , which gives certain pole/zero condition
similarly for a purely imaginary signal ,
$x(n)$ =$-x^*(n)$ , if we take Z-Transform on both sides , $X(z)$=$-X^*(z^*)$
which gives similar pole/zero condition as that of real signal(poles and zeros are not effected by negative sign).
But My professor says if the poles/zeros are symmetric with respect to real axis, then it is a real signal. But i am getting same condition for both real and imaginary signal.
Can anyone help me? (examples might be helpful)