How, with complete markets, do we have a representative agent?
It depends on what you want from a representative agent. What you get is a representative agent at the given prices. For any two commodities, you have relative prices. This is where market completeness comes in. All you have to do now is find a well-behaved utility function whose marginal rate of substitution between the commodities corresponds to the relative prices. You can even take the utility function to be linear:
$$u(x_1,x_2,\ldots,x_l)=\sum_{i=1}^l x_i/p_i.$$
Of course, the resulting "representative agent" is utterly useless for any comparative statics exercise or any welfare analysis.