represent a communication signal on complex envelope form

Hi everyone:
we know that The communications signal may be written as the real part of a complex waveform with real and
imaginary parts, s(t)=Re{ a(t) exp(j theta) } with complex envelope {a(t) exp(j phi)},my question is why we represent the signal on the In_phase and quadrature form i.e on the I&Q form what is the benefits of this representation ?