A complex number
consists of a real part
and an imaginary part
.
(We choose
and
to be real numbers.)
is the square root of -1.
The complex conjugate of
is
.
(Just change the sign of all the
.)
The absolute square of a complex number is calculated by multiplying it by its complex conjugate.
We will use complex exponentials all the time.
We can write
and
.
As with other exponentials, we can multiply them by adding the exponents.
Jim Branson 2013-04-22