As opposed to complex exponentials which oscillate, real exponentials (Figure 2.3) decay.
The quantity τ is known as the exponential's time constant, and corresponds to the time required for the exponential to decrease by a factor of , which approximately equals 0.368. A decaying complex exponential is the product of a real and a complex exponential.
In the complex plane, this signal corresponds to an exponential spiral. For such signals, we can define complex frequency as the quantity multiplying t.