Math 15200 Lesson 13 Section 1.4 - Mixed Review Worksheet
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5MA 15200
Lesson 13
Section 1.4
I
The imaginary unit i
Even though it does not seem logical to speak of square roots of negative numbers, they
are important and play a role in some algebra and science fields.
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A number i is defined to be the solution of the equation
x
=
−
1
. Therefore ...
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The imaginary unit i is defined by
, 1
where
1
.
i
=
−
i
=
−
A square root of a negative number can be represented using i in the following manner.
−
36
=
36
⋅
−
1
=
i 6
Ex 1: Write each number using the imaginary unit.
a
)
−
100
49
b
)
−
4
c
)
−
18
II
The Set of Complex Numbers
A new set of numbers is created using imaginary numbers. A complex number is
formed by adding a real number to an imaginary number.
The following diagram shows the relationship among these sets of numbers.
Complex Numbers
2
2
−
, 3
i
+
i
4 ,
−
i
3
3
Real Numbers
Imaginary Numbers
11
, 4
i i
, 7
−
13
,
2
, 5
,
−
45
,
. 2
86
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A complex number is written in a + bi form (standard form), where a is the 'real part' and
bi is the 'imaginary part'.
If a = 0 (0+ bi), the number is a pure imaginary number.
If b = 0, (a + 0i), the number is a pure real number.
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