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.
is defined to be the letter
Since the square root of
negative one is now defined to be the letter
, it is now possible to simplify a
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 a + bi form and the two numbers together form what is called a complex number.
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.
so if we substitute negative one in the place of the
is now a complex number of the form a + bi.
An interesting result occurs when multiplying two Complex number conjugates. Consider multiplying the conjugate binomials INSERT REMAINING EXPLANATION
The views and
opinions expressed in this page are strictly those of Mary Lou Baker. This page was
The views and
opinions expressed in this page are strictly those of Mary Lou Baker.
This page was edited on 16-Sep-2008