Why are frequencies represented as complex numbers?

In a FFT, the resulting frequencies represent both magnitude and phase. Since each frequency element in the output array of an FFT essentially just describes the SIN wave at each frequency interval, shouldn't it just be magnitude that we need? What is the significance of the phase represented in the imaginary part of the complex number?

To clarify my question, to be able to put a meaning to the phase of a wave, I need a reference point or reference wave.

When an FFT reports the phase for each sin wave in the resulting frequency domain output, what is the reference wave with respect to which it is reporting the phase?

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