Lovely picture of this water bird. Though your title implies that I should accept the blue of the eye as the complement to the orange, it just doesn't seem that color is answering the challenge very well.
This is a beautiful high contrast image, but I don't see complimentary colors from any color wheel. I would need purple or blue or possibly green in order for that to be the case as orange of the beak and feet is the only true color. The contrast is great with the black and white. I love the lighting and the dark background, but the opposite color just isn't there. :~(