This applet shows how the superposition of two [i]complex[/i] exponential functions of time can result in a [i]real[/i] oscillation. Click on the "play" button on the bottom left to show the two complex numbers [math]u[/math] and [math]v[/math] being added - note that they are mutual complex conjugates - and watch their superposition [math]w[/math] oscillate on the real axis.