No, there is no error.

With the reals you expect

(1) a < b and 0 < c imply ac < bc.

With the complex numbers, either assumption

0 < i or 0 < -i

leads to a contradiction if (1) is assumed to work in the complex case as well. Because, as you point out, i = -1. Which leads to a change of direction in the inequality. The trouble is this direction change is not implied by (1).