Unfortunately this is somewhat misleading and even wrong at times.<p>A crucial aspect that many of the I/Q explanations miss is, that the I/Q representation (which is really phasor notation) is a feature of modulation onto a carrier wave, not baseband.<p>So the example starts of with drawing the sine wave and say we don't know the full wave, because we don't know if frequencies are positive or negative and because it's hard to determine the power (not even sure what he/she means there). That is wrong and directly contradicts Nyquist theory, if we sample a signal at twice it's maximum frequency we can fully reconstruct it. The reason the explanation goes wrong is because they bring in negative frequencies. Negative frequencies do not exist!<p>This is where the phasor/IQ representation comes in. If we modulate a signal onto a carrier wave, in other words we have a wave at some frequency and we modulate that wave in amplitude/phase/frequency, we generate frequencies higher and lower than that carrier frequency. The modulation can have components that correspond to the sine or cosine of that carrier wave. Importantly these components are orthogonal, so can carry independent data. That's where we use the phasor representation (IQ-modulation), and remove the carrier wave and represent this "artificial" baseband signal using complex numbers or sine or cosine components, or positive/negative frequencies (all these are equivalent). But it is important to remember that this is just a representation of a signal modulated onto a carrier as if there was no carrier.<p>That's where this explanation goes wrong.