  Let $0,1\ne m\in Z$ and $\alpha=\sqrt[8]{m}$. According to the results of I.
Ga\'al and L. El Fadil, $\alpha$ generates a power integral basis in
$K=Q(\alpha)$, if and only if $m$ is square-free and $m\not\equiv 1\;(\bmod\;
4)$. In the present paper we consider totally complex pure octic fields, that
is the case $m<0$, with $m$ satisfiying the above property. In this case
$(1,\alpha,\alpha^2,\ldots,\alpha^7)$ is an integral basis. Our purpose is to
investigate whether $K$ admits any other generators of power integral bases,
inequivalent to $\alpha$. We present an efficient method to calculate
generators of power integral bases in this type of fields with coefficients
$<10^{200}$ in the above integral basis. We report on the results of our
calculation for this type of fields with $0>m>-5000$, which yields 2024 fields.
