The paper presents three algorithms to synthesize a dynamic controller for a doubly-fed induction generator (DFIG). In each case, the pole placement approach is used to compute the parameters of a feedback controller that regulates the active and reactive powers produced using the rotor voltages. Due to the special structure of the DFIG's model, the analysis and design of the feedback control loop are simplified by transforming its representation into an equivalent system with complex coefficients and half the number of states. This approach yields analytic solutions of the problem with remarkable simplicity. The complex framework facilitates the direct placement of the DFIG system poles in the left half-plane, which ensures stability and performance of the closedloop system. Additionally, this framework can be used to evaluate the robustness properties of the closed-loop systems. The ability of the synthesized controllers to provide a desirable dynamic and steady-state response is investigated through experiments on a laboratory testbed.