Zeros of the Macdonald function of complex order

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