The Imaginary Unit
is defined as
i
=
.
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The reason for the name
"imaginary"
numbers is that when these numbers were first proposed several hundred years ago,
people could not
"imagine" such a
number. |
It is said that the term "imaginary" was
coined by René Descartes in the seventeenth century and was meant to
be a derogatory reference since, obviously, such numbers did not
exist. Today, we find the imaginary unit being used in
mathematics and science. Electrical engineers use the imaginary
unit (which they represent as j ) in the study of electricity.
Imaginary numbers occur when a quadratic equation has
no roots
in the set of real numbers.
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* i
=
or
-
i = -
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An imaginary number is a number whose square is negative.
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A pure imaginary number can be
written in bi
form where
b is
a real number and
i
is
.
Examples:
pure imaginary
numbers |
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A complex number
is any number that can be written in the
standard
form
a + bi,
where a and
b are real numbers and
i is
the
imaginary unit.
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A
complex number
is a real number
a,
or a pure imaginary number
bi,
or the sum of both.
Note these examples of complex numbers written
in standard a
+
bi
form:
2 + 3i, -5 + 0i
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Complex Number:
standard a +
bi form
|
a |
bi |
|
7 + 2i |
7 |
2i |
|
1 - 5i |
1 |
- 5i |
|
8i |
0 |
8i |
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The set of real numbers
and the set of imaginary numbers
are
subsets of the set of
complex numbers.
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Check out how to use your
TI-83+/84+ graphing calculator with
complex numbers.
Click here. |
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