AnswersPrecalculusPolar Form of Complex Numbers

Polar Form of Complex Numbers — Quiz Answers

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1
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Which graph represents negative 4 plus 3 i ?

A
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is at (negative 4, 3).
B
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is at (negative 3, 4).
C
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is at (3, negative 4).
D
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is at (4, negative 3).
2
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What is the argument of z is equal to 1 over 16 minus the fraction with numerator square root of 3 and denominator 16 i ?

A
pi over 3
B
pi over 6
C
negative pi over 6
D
negative pi over 3
3

If z is equal to 13 minus 7 i , what is the value of absolute value of z ?

A
6
B
square root of 218
C
20
D
2 square root of 30
4

What is the polar form of negative 2 square root of 3 minus 6 i ?

A
2 square root of 6 open paren cosine of open paren 4 pi over 3 close paren plus i sine open paren 4 pi over 3 close paren close paren
B
2 square root of 6 open paren cosine of open paren 2 pi over 3 close paren plus i sine open paren 2 pi over 3 close paren close paren
C
4 square root of 3 open paren cosine of open paren 4 pi over 3 close paren plus i sine open paren 4 pi over 3 close paren close paren
D
4 square root of 3 open paren mathrm cosine open paren 2 pi over 3 close paren plus i sine open paren 2 pi over 3 close paren close paren
5

What is the rectangular form of 12 times open paren cosine of pi plus i sine pi close paren ?

A
12
B
negative 12 plus i
C
negative 12
D
12 plus i
6

What is the rectangular form of 17 times open paren cosine of open paren 315 degrees close paren plus i sine open paren 315 degrees close paren close paren ?

A
the fraction with numerator 17 square root of 2 and denominator 2 plus the fraction with numerator 17 square root of 2 and denominator 2 i
B
negative the fraction with numerator 17 square root of 2 and denominator 2 plus the fraction with numerator 17 square root of 2 and denominator 2 i
C
negative the fraction with numerator 17 square root of 2 and denominator 2 minus the fraction with numerator 17 square root of 2 and denominator 2 i
D
the fraction with numerator 17 square root of 2 and denominator 2 minus the fraction with numerator 17 square root of 2 and denominator 2 i
7

What is the polar form of negative 9 square root of 3 plus 9 i ?

A
324 times open paren cosine of open paren 120 degrees close paren plus i sine open paren 120 degrees close paren close paren
B
324 times open paren cosine of open paren 150 degrees close paren plus i sine open paren 150 degrees close paren close paren
C
18 times open paren cosine of open paren 120 degrees close paren plus i sine open paren 120 degrees close paren close paren
D
18 times open paren cosine of open paren 150 degrees close paren plus i sine open paren 150 degrees close paren close paren
8

What is the rectangular form of z is equal to 40 times open paren cosine of open paren 7 pi over 6 close paren plus i sine open paren 7 pi over 6 close paren close paren ?

A
z is equal to negative 20 square root of 3 minus 20 i
B
z is equal to 20 square root of 3 minus 20 i
C
z is equal to 20 minus 20 i square root of 3
D
z is equal to negative 20 minus 20 i square root of 3
9

Which graph represents 2 times open paren cosine of open paren 2 pi over 3 close paren plus i sine open paren 2 pi over 3 close paren close paren ?

A
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is around (1, 1.75).
B
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is around (negative 1, 1.75).
C
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is around (negative 0.5, 1).
D
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is around (0.5, 1).
10

For the complex number z is equal to 12 plus i , what is line segment z ?

A
negative 12 plus i
B
12 plus i
C
12 minus i
D
negative 12 minus i

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