Here are a couple of games of complex countdown in action to give you some ideas of how to get started. We use square brackets [ ... ] to show that we are using up one of the original cards.
One possible solution here is
[8+9i] + [-2 - 9i] + [0-7i] + ([8i]/[4-0i])
One possible solution is [-1 - 4i] - [-8i]/(/[-2])
Arg[-4i] - (Re[7+1i] x Im[-8i]) + [-1]