Complex Numbers Worksheet - Appendix F, Cengage Page 3
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APPENDIX F
Complex Numbers
EXAMPLE 2
Multiplying Complex Numbers
a.
2
3
2i 3
2i
9
6i
6i
4i
Product of binomials
9
4
1
2
i
1
9
4
Simplify.
13
Write in standard form.
b.
2
2
3
2i
9
6i
6i
4i
Product of binomials
9
12i
4
1
2
i
1
9
4
12i
Group like terms.
5
12i
Write in standard form.
Notice in Example 2(a) that the product of two complex numbers can be a real num-
ber. This occurs with pairs of complex numbers of the form
a
bi
and
a
bi,
called
complex conjugates.
2
2
2
a
bi a
bi
a
abi
abi
b
i
2
2
a
b
1
2
2
a
b
To write the quotient of
a
bi
and
c
di
in standard form, where c and d are
not both zero, multiply the numerator and denominator by the complex conjugate of
the denominator to obtain
a
bi
a
bi
c
di
c
di
c
di
c
di
ac
bd
bc
ad i
.
2
2
c
d
EXAMPLE 3
Writing a Quotient of Complex Numbers in Standard Form
Multiply numerator and
2
3i
2
3i
4
2i
denominator by complex
4
2i
4
2i
4
2i
conjugate of denominator.
2
8
4i
12i
6i
Expand.
2
16
4i
8
6
16i
2
i
1
16
4
2
16i
Simplify.
20
1
4
i
Write in standard form.
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