Complex sentence: It is convenient that these two can be treated as the real and imaginary components of a complex quantity and use the Fourier theory to transform the measured time domain signal into the frequency domain representation.
Split into simpler sentences: It is convenient that these two can be treated as the real and imaginary components of a complex quantity. The reason for this representation is that one can now use Fourier theory to transform the measured time domain signal into the frequency domain representation.