Complex Numbers
It is often stated that the square root
of a negative (radicand) number is "not a Real number" since no Real
number when squared would produce a negative product. While it is
true that this number is not "Real," it is none the less a number.
In Algebra,
is defined to be the letter
i.
Since the square root of
negative one is now defined to be the letter
i
, it is now possible to simplify a
radical with
a negative radicand, such as
.
Often when a
Real number and an
imaginary number are in the same expression the Real number is first
and the imaginary number follows. This form is commonly known as the
When multiplying complex numbers, the result may be another complex number. For example, consider the product of the following binomials:
Normally we would combine the like terms and arrive at the product of Since the complex number is left in the form a + bi, the must then be addressed.
since
so if we substitute negative one in the place of the
is now a An interesting result
occurs when multiplying two Complex number conjugates. Consider
multiplying the conjugate binomials
The views and
opinions expressed in this page are strictly those of Mary Lou Baker. This page was edited on 16-Sep-2008 |