Complex Numbers Worksheet
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2
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41.5 Complex Numbers
In this section you will learn to:
• add, subtract, multiply and divide complex numbers
• simplify complex numbers
• find powers of i
• solve quadratic equations with complex roots
2
The imaginary unit i is defined as
i
1
, where
i
1
.
=
−
=
−
The set of all numbers in the form a + bi with real numbers a and b and i, the imaginary unit, is called
the set of complex numbers . ( Standard form for a complex number is a + bi .)
THE COMPLEX NUMBER SYSTEM
Real
Imaginary
Numbers
Numbers
Rational Numbers
Irrational Numbers
Example 1: Simplify each imaginary number below:
−
12
−
9
= _____
−
36
= _____
−
8
= _____
−
27
= ______
= _____
25
Equality of Complex Numbers:
a
+
bi
=
c
+
di
if and only if
a =
c
and
b =
. d
Addition of Complex Numbers:
(
a
bi
)
(
c
di
)
(
a
c
)
(
b
d
)
i
+
+
+
=
+
+
+
Subtraction of Complex Numbers:
(
a
bi
)
(
c
di
)
(
a
c
)
(
b
d
)
i
+
−
+
=
−
+
−
Multiplication of Complex Numbers:
(
a
bi
)(
c
di
)
(
ac
bd
)
(
ad
bc
)
i
+
+
=
−
+
+
NOTE : Add, subtract, or multiply complex numbers as if they were binomials.
Page 1 (Section 1.5)
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