Math 15200 Lesson 13 Section 1.4 - Mixed Review Worksheet Page 2
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1
2
3
4
5Therefore, every real number can be written as a complex number and every imaginary
number can be written as a complex number.
If b is contains a radical, we usually write the i before the radical. These are examples of
2
π
complex numbers:
2
−
, 3
i
4
+
i
,
−
, 8
, 5
i
6
+
i
, 2
−
3
i
5
3
III
Operations with Complex Numbers
Basically, combine like
(
a
+
bi
)
+
(
c
+
di
)
=
(
a
+
c
)
+
(
b
+
d
)
i
terms.
(
a
+
bi
)
−
(
c
+
di
)
=
(
a
−
c
)
+
(
b
−
d
)
i
Ex 2: Add or subtract and write in standard form.
)
6 (
2
)
3 (
14
)
a
−
i
+
+
i
=
−
+
3
2
b
)
3
i
−
7
i
=
4
3
c
)
(
14
−
−
16
)
−
(
−
81
−
) 2
=
)
3 (
12
)
(
17
49
)
d
i
+
+
−
−
=
e
)
4 (
−
2
i
)
−
6 (
+
3
i
)
+
(
12
−
2
i
)
=
Note: You must change the square roots of negative numbers to pure imaginary number
before adding or subtracting.
IV
Multiplication of Complex Numbers
Basically, use FOIL when
multiplying and remember
2
(
a
+
bi
)(
c
+
di
)
=
ac
+
adi
+
bci
+
bdi
2
to simplify
i
=
−
1
and
2
=
ac
+
adi
+
bci
−
bd
(
i
=
−
) 1
combine 'like' terms.
=
(
ac
−
bd
)
+
(
ad
+
bc
)
i
2
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