Complex Numbers Worksheet - Appendix F, Cengage Page 2
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APPENDIX F
Complex Numbers
The additive identity in the complex number system is zero (the same as in the
real number system). Furthermore, the additive inverse of the complex number
a
bi
is
a
bi
a
bi
Additive inverse
So, you have
a
bi
a
bi
0
0i
0.
EXAMPLE 1
Adding and Subtracting Complex Numbers
a.
3
i
2
3i
3
i
2
3i
Remove parentheses.
3
2
i
3i
Group like terms.
3
2
1
3 i
5
2i
Write in standard form.
b.
2i
4
2i
2i
4
2i
Remove parentheses.
4
2i
2i
Group like terms.
4
Write in standard form.
c.
3
2
3i
5
i
3
2
3i
5
i
3
2
5
3i
i
0
2i
2i
Notice in Example 1(b) that the sum of two complex numbers can be a real
number.
Many of the properties of real numbers are valid for complex numbers as well.
Here are some examples.
Associative Properties of Addition and Multiplication
Commutative Properties of Addition and Multiplication
Distributive Property of Multiplication over Addition
Notice below how these properties are used when two complex numbers are
multiplied.
a
bi c
di
a c
di
bi c
di
Distributive Property
Rather than trying to
STUDY TIP
memorize the multiplication rule at the
2
ac
ad i
bc i
bd i
Distributive Property
right, you can simply remember how the
ac
ad i
bc i
bd
1
Definition of i
Distributive Property is used to multiply
two complex numbers. The procedure is
ac
bd
ad i
bc i
Commutative Property
similar to multiplying two polynomials
ac
bd
ad
bc i
and combining like terms.
Associative Property
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