
3 2
Analog Electronics
through it. However, j also possesses another
significance. You may recall (in connection with
Figure 1.7) that when we saw that the differential
(the rate of change) of a sine wave was another
waveform of exactly the same shape, we suspected
that the sinusoidal function was somehow con-
nected with the exponential function. Well, it
turns out that
eJ" = cos θ + j sin θ
e-J« = cos θ - j sin θ
(2.1)
This is known as Eulers identity. So we can
represent sinusoidal voltage waveforms like V sin
in exponential form, since using (2.1) we can
write
Sin ωί =
-
2j
and cos ω/ =
We can also allow for sine waves of increasing or
decreasin ...