Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Find the product. Write the
product in rectangular form, using exact values. [ 3(cos 45° + i sin 45°)] [2(cos
90° + i sin 90°)]
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2.
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Find the product. Write the
product in rectangular form, using exact values. [4(cos 150° + i sin 150°)] [6(cos
330° + i sin 330°)]
a. | -12 + 12 i | c. | 12
+ 12i | b. | 24i | d. | 24 |
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3.
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Find the product. Write the
product in rectangular form, using exact values. [4(cos 210° + i sin
210°)] [5(cos 120° + i sin 120°)]
a. | 10 + 10 i | c. | -10 - 10 i | b. | -10 + 10i | d. | 10 -
10i |
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4.
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Find the product. Write the
product in rectangular form, using exact values. [8 cis 240°] [6 cis
330°]
a. | -12 + 12 i | c. | 24i | b. | 24 | d. | -24 -
24i |
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5.
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Find the product. Write the
product in rectangular form, using exact values. [4 cis 315°] [6 cis
225°]
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6.
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Find the quotient and write
in rectangular form. First convert the numerator and denominator to trigonometric
form.
a. |  +  i | c. | 1 +  i | b. | 8 + 8 i | d. |  +  i |
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7.
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Find the quotient and write
in rectangular form. First convert the numerator and denominator to trigonometric
form.
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8.
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Find the quotient and write
in rectangular form. First convert the numerator and denominator to trigonometric
form.
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9.
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Find the quotient and write
in rectangular form. First convert the numerator and denominator to trigonometric
form.
a. | -4 i | c. | - 2 - 2
i | b. | -4 | d. | -4 - 4i |
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10.
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Find the quotient and write
in rectangular form. First convert the numerator and denominator to trigonometric
form.
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11.
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Find the quotient and write
in rectangular form. First convert the numerator and denominator to trigonometric
form.
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12.
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Find the quotient and write
in rectangular form. First convert the numerator and denominator to trigonometric
form.
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13.
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Perform the indicated
operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
[5(cos 20° +
i sin 20°)][4(cos 10° + i sin 10°)]
a. | 17.3205 +
10.0000i | c. | 0.8660 +
0.5000i | b. | 0.5000 + 0.8660i | d. | 10.0000 + 17.3205i |
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14.
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Perform the indicated
operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
( 12 cis
13.5°)( 2 cis 7.5°)
a. | 22.4059 +
8.6008i | c. | -6.5728 +
10.0399i | b. | 20.0797 + 22.4059i | d. | 1.6733 - 1.0955i |
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15.
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Perform the indicated
operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
a. | -23.4923 +
8.5505i | c. | -4.6985 +
1.7101i | b. | 8.5505 - 23.4923i | d. | 4.3412 + 24.6202i |
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16.
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The current I in a circuit with
voltage E, resistance R, capacitive reactance  and inductive reactance
 is
I = 
Find I if
E = 3 (cos 45° + i sin 45°), R = 4,
 = 4, and  =
2.
Give your answer in rectangular form.
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17.
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In a parallel electrical
circuit, the impedance Z can be calculated using the equation
 = 
where  and  are the
impedances for the branches of the circuit. The phase angle measures the phase difference
between the voltage and the current in an electrical circuit. If the impedance Z is expressed
in the form  , è can
be determined by the equation tan  . Determine the phase angle
è (in degrees) for a parallel circuit in which 
and 
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