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Over Lesson 5–3
Solve x 2 – x = 2 by factoring.
A. 2, –1
B. 1, 2
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A
B
C
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D
D
A
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B
D. –1, 1
C
C. 1, 1
A.
B.
C.
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D.
Over Lesson 5–3
Solve c 2 – 16c + 64 = 0 by factoring.
A. 2
B. 4
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A
B
C
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D
D
A
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B
D. 12
C
C. 8
A.
B.
C.
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D.
Over Lesson 5–3
Solve z 2 = 16z by factoring.
A. 1, 4
B. 0, 16
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A
B
C
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D
D
A
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B
D. –16
C
C. –1, 4
A.
B.
C.
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D.
Over Lesson 5–3
Solve 2x 2 + 5x + 3 = 0 by factoring.
A.
A
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B
D.
A
B
C
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D
D
C. –1
A.
B.
C.
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D.
C
B. 0
Over Lesson 5–3
Write a quadratic equation with the roots –1 and 6
in the form ax 2 + bx + c, where a, b, and c are
integers.
A. x2 – x + 6 = 0
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B
D. x2 – 6x + 1 = 0
A
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A
B
C
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D
D
C. x2 – 5x – 6 = 0
C
B. x2 + x + 6 = 0
A.
B.
C.
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D.
• imaginary unit
• pure imaginary number
• complex number
• complex conjugates
Definitions
The imaginary unit is
The imaginary number is
i2
1
i
For any positive real numbers b
-b
2
b
2
1 ib
1
Square Roots of Negative Numbers
A.
Answer:
A.
A.
B.
0%
B
A
0%
A
B
C
0%
D
D
D.
C
C.
A.
B.
C.
0%
D.
Square Roots of Negative Numbers
B.
Answer:
B.
A.
B.
0%
B
A
0%
A
B
C
0%
D
D
D.
C
C.
A.
B.
C.
0%
D.
Products of Pure Imaginary Numbers
A. Simplify –3i ● 2i.
–3i ● 2i = –6i 2
= –6(–1)
=6
Answer: 6
i 2 = –1
A. Simplify 3i
5i.
A. 15
B. –15
0%
B
A
0%
A
B
C
0%
D
D
D. –8
C
C. 15i
A.
B.
C.
0%
D.
Products of Pure Imaginary Numbers
B.
1
4
1 2
2
Answer:
6
6
6
B. Simplify
.
A.
B.
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B
A
0%
A
B
C
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D
D
D.
A.
B.
C.
0%
D.
C
C.
Equation with Pure Imaginary Solutions
Solve 5y 2 + 20 = 0.
5y 2 + 20 = 0
5y 2 = –20
y 2 = –4
Original equation
Subtract 20 from each side.
Divide each side by 5.
Take the square root of
each side.
Answer: y = 2i
Solve 2x 2 + 50 = 0.
C.
5
D.
25
0%
0%
A.
B.
C.
0%
D.
A
B
C
0%
D
D
25i
C
B.
B
5i
A
A.
Equate Complex Numbers
Find the values of x and y that make the equation
2x + yi = –14 – 3i true.
Set the real parts equal to each other and the imaginary
parts equal to each other.
2x = –14
Real parts
x = –7
Divide each side by 2.
y = –3
Imaginary parts
Answer: x = –7, y = –3
Find the values of x and y that make the equation
3x – yi = 15 + 2i true.
A. x = 15
y=2
0%
B
0%
A
D. x = 5
y = –2
A
B
C
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D
D
C. x = 15
y = –2
A.
B.
C.
0%
D.
C
B. x = 5
y=2
Add and Subtract Complex Numbers
A. Simplify (3 + 5i) + (2 – 4i).
(3 + 5i) + (2 – 4i) = (3 + 2) + (5 – 4)i
=5+i
Answer: 5 + i
Commutative and
Associative
Properties
Simplify.
A. Simplify (2 + 6i) + (3 + 4i).
A. –1 + 2i
B. 8 + 7i
0%
B
A
0%
A
B
C
0%
D
D
D. 5 + 10i
C
C. 6 + 12i
A.
B.
C.
0%
D.
Add and Subtract Complex Numbers
B. Simplify (4 – 6i) – (3 – 7i).
(4 – 6i) – (3 – 7i) = (4 – 3) + (–6 + 7)i Commutative and
Associative
Properties
=1+i
Answer: 1 + i
Simplify.
B. Simplify (3 + 2i) – (–2 + 5i).
A. 1 + 7i
B. 5 – 3i
0%
B
A
0%
A
B
C
0%
D
D
D. 1 – 3i
C
C. 5 + 8i
A.
B.
C.
0%
D.
Multiply Complex Numbers
(1 + 4i)(3 – 6i)
= 1(3) + 1(–6i) + 4i(3) + 4i(–6i)
FOIL
= 3 – 6i + 12i – 24i 2
Multiply.
= 3 + 6i – 24(–1)
i 2 = –1
= 27 + 6i
Add.
Answer: 27 + 6i
(1 – 3i)(3 + 2i)
A. 4 – i
B. 9 – 7i
C. –2 – 5i
D. 9 – i
A.
B.
C.
D.
A
B
C
D
Divide Complex Numbers
A.
3 – 2i and 3 + 2i are
conjugates.
Multiply.
i2 = –1
a + bi form
Answer:
A.
A.
B. 3 + 3i
0%
A
B
C
0%
D
D
A
0%
B
D.
C
C. 1 + i
A.
B.
C.
0%
D.
Divide Complex Numbers
B.
Multiply by
Multiply.
i2 = –1
a + bi form
Answer:
.
B.
A.
A
0%
0%
B
D.
A
B
C
0%
D
D
C.
A.
B.
C.
0%
D.
C
B.