Zeros of the Macdonald function of complex order

The z  -zeros of the modified Bessel function of the third kind _Kν(z)$K_{\nu }(z)$, also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order ν$\nu$. Approximate expressions for the zeros, applicable in the cases of very small or very large |ν|$\left|\nu \right|$, are given. The behaviour of the zeros for varying |ν|$\left|\nu \right|$ or argν$\arg \nu$, obtained numerically, is illustrated by means of some graphics.