Download MAC 1114 Module Test 10

MAC 1114 Module Test 10
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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Perform the indicated operations. Simplify the answer.
1) -11 · -11
A) 11i
B) 11
C) -11i
D) -11
Answer: D
Objective: (8.1) Multiply/Divide Expression with Negative Radicands
In work with alternating current, complex numbers are used to describe current I, voltage E, and impedance Z. These
three quantities are related by the equation E = IZ. Solve the equation E = IZ for the missing variable.
2) I = 7 + 2i, Z = 5 + 4i
A) E = 27 + 38i
B) E = 35 + 46i
C) E = 35 + 8i
D) E = 43 + 38i
Answer: A
Objective: (8.1) Solve Apps: Current, Voltage, Impedance
Find the quotient. Write the answer in standard form.
3) 8 + 4i
6 - 9i
A) 4 + 32 i
39
39
B) 28 + 16 i
13
13
C) - 4 + 32 i
45
45
D) - 28 + 32 i
15
45
Answer: A
Objective: (8.1) Divide Complex Numbers
Identify the number as real, complex, pure imaginary, or none of these. More than one of these descriptions may
apply.
4) -2
A) Complex
B) Real, complex
C) Complex, pure imaginary
D) None of these
Answer: C
Objective: (8.1) Identify Number as Real, Complex, or Pure Imaginary
Indicate whether the statement is true always, sometimes, or never.
5) The product of a pair of complex conjugates is a real number.
A) Always
B) Sometimes
C) Never
Answer: A
Objective: (8.1) Know Concepts: Complex Numbers
Find the product. Write the answer in standard form.
6) i(2 - 4i)(9 - 3i)
A) -42 - 6i
B) 30 - 30i
C) 42 + 6i
Answer: C
Objective: (8.1) Multiply Complex Numbers
1
D) 12i3 + 42i2 + 18i
Simplify the power of i.
7) i-22
A) i
B) -1
D) -i
C) 1
Answer: B
Objective: (8.1) Simplify Power of i
Indicate whether the statement is true always, sometimes, or never.
8) When i is raised to an even power, the result is -1.
A) Always
B) Sometimes
C) Never
Answer: B
Objective: (8.1) Know Concepts: Complex Numbers
Solve the equation.
9) 4x2 - 9x = -6
A) -9 ± 15
8
B) 9 ± i 15
8
C) -9 ± i
8
15
D) 9 ±
15
8
Answer: B
Objective: (8.1) Solve Quadratic Equation (Complex Solutions)
Find the resultant (sum) of the complex numbers. Express in rectangular form a + bi.
10) -7 + 2i, -8
A) -15 + 2i
B) 1 + 2i
C) 1 - 6i
Answer: A
Objective: (8.2) Find Resultant (Sum) of Pair of Complex Numbers
Graph the terminal point of the given complex number.
11) 3 + 2i 7
y
10
5
-10
-5
5
10 x
-5
-10
2
D) -15 - 6i
A)
B)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
C)
5
10 x
5
10 x
D)
y
-10
y
10
10
5
5
-5
5
10 x
-10
-5
-5
-5
-10
-10
Answer: B
Objective: (8.2) Graph Complex Number
Perform the conversion, using a calculator as necessary.
12) Convert 125(cos 25° + i sin 25°) to rectangular form (i.e., a + bi).
A) 123.90035148 - 16.54396876i
B) 113.28847338 + 52.82728272i
C) 52.82728272 + 113.28847338i
D) 25.00000000 + 125.00000000i
Answer: B
Objective: (8.2) Tech: Convert Between Trigonometric and Rectangular Form
Graph the terminal point of the given complex number.
3
13) -1 + i
y
6
4
2
-6
-4
-2
2
4
x
6
-2
-4
-6
A)
B)
y
-6
-4
y
6
6
4
4
2
2
-2
2
4
6
x
-6
-4
-2
-2
-2
-4
-4
-6
-6
C)
2
4
6
x
2
4
6
x
D)
y
-6
-4
y
6
6
4
4
2
2
-2
2
4
6
x
-6
-4
-2
-2
-2
-4
-4
-6
-6
Answer: C
Objective: (8.2) Graph Complex Number
Write the complex number in rectangular form.
14) 3 cis 270°
A) -i 3
B) -i
C) -3i
Answer: A
Objective: (8.2) Convert Trigonometric to Rectangular Form (Degrees)
4
D) -
3
Write the complex number in trigonometric form r(cos θ + i sin θ), with θ in the interval [0°, 360°).
15) - 7 - i 7
A) 14( cos 45° + i sin 45°)
B) 14( cos 135° + i sin 135°)
C) 14( cos 225° + i sin 225°)
D) 14( cos 315° + i sin 315°)
Answer: C
Objective: (8.2) Convert Rectangular to Trigonometric Form
Find the resultant (sum) of the complex numbers. Express in rectangular form a + bi.
16) 4i, -8i
A) -4i
B) 4 - 8i
C) -4
D) -8 + 4i
Answer: A
Objective: (8.2) Find Resultant (Sum) of Pair of Complex Numbers
17) -6 - 5i, -3i
A) -6 - 8i
B) -6 - 2i
C) -14i
D) -9 - 5i
Answer: A
Objective: (8.2) Find Resultant (Sum) of Pair of Complex Numbers
Write the complex number in rectangular form.
18) 9 cos π + i sin π
2
2
A) 9i
C) -9i
B) 9
D) -9
Answer: A
Objective: (8.2) Convert Trigonometric to Rectangular Form (Radians)
Give the rectangular form of the complex number whose terminal point is represented in the graph.
19)
5
y
4
3
2
1
-4 -3 -2 -1
-1
1
2
3
4
x
-2
-3
-4
-5
A) -3 - 5i
B) -5 - 3i
C) -3 + 5i
D) -5 + 3i
Answer: B
Objective: (8.2) Find Rectangular Form of Complex Number from Graph
Write the complex number in trigonometric form r(cos θ + i sin θ), with θ in the interval [0°, 360°).
20) 4i
A) 4(cos 90° + i sin 90°)
B) 4(cos 0° + i sin 0°)
C) 4(cos 270° + i sin 270°)
D) 4(cos 180° + i sin 180°)
Answer: A
Objective: (8.2) Convert Rectangular to Trigonometric Form
5