^{16}The necessity of a shared frequency is easily understood if one considers a case of two sine waves at different
frequencies: their respective phasors would spin at different speeds. Given two phasors spinning at different speeds, the
angle separating those two phasors would be constantly changing. It is only when two phasors spin around at
precisely the same speed that we can sensibly talk about there being a fixed angular displacement between
them. Fortunately this is the usual case in AC circuit analysis, where all voltages and currents share the same
frequency.