Complex sentence: The Fourier transform of a function of time is a complex-valued function of frequency, whose complex modulus of the Fourier transform represents the amount of that frequency present in the original function, and whose complex argument is the phase offset of that frequency.
Split into simpler sentences: The Fourier transform of a function of time is a complex-valued function of frequency. The complex modulus of the Fourier transform represents the amount of that frequency present in the original function, and the complex argument is the phase offset of that frequency.