The passage from sines and cosines to complex exponentials makes it necessary for the Fourier coefficients to be complex-valued. The usual interpretation of this complex number is that it gives both the amplitude (or size) of the wave present in the function and the phase (or the initial angle) of the wave. This passage also introduces the need for negative "frequencies". (E.G. If θ were measured in seconds then the waves e and e would both complete one cycle per second—but they represent different frequencies in the Fourier transform. Hence, frequency no longer measures the number of cycles per unit time, but is closely related.)