AnswersMath 4Multiply and Divide Complex Numbers

Multiply and Divide Complex Numbers — Quiz Answers

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1
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Which statement describes how to geometrically determine the product of z is equal to 25 minus i and w is equal to square root of 3 plus 3 i on the complex plane?

A
Stretch z by a factor of square root of 3 and rotate 30 degrees counterclockwise.
B
Stretch z by a factor of 2 square root of 3 and rotate 30 degrees counterclockwise.
C
Stretch z by a factor of square root of 3 and rotate 60 degrees counterclockwise.
D
Stretch z by a factor of 2 square root of 3 and rotate 60 degrees counterclockwise.
2
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For z is equal to negative 3 minus 5 i , which graph shows z and the product of z times i ?

A
Image with description Complex plane with the horizontal axis labeled real and the vertical axis labeled imaginary. The x-axis is labeled from negative 6 to 6 in increments of 2, and the y-axis is labeled from negative 6 to 6 in increments of 2. Point z is plotted at (negative 3 comma negative 5). Point z times i is plotted at (3 comma negative 5).
B
Image with description Complex plane with the horizontal axis labeled real and the vertical axis labeled imaginary. The x-axis is labeled from negative 6 to 6 in increments of 2, and the y-axis is labeled from negative 6 to 6 in increments of 2. Point z is plotted at (negative 3 comma negative 5). Point z times i is plotted at (negative 5 comma 3).
C
Image with description Complex plane with the horizontal axis labeled real and the vertical axis labeled imaginary. The x-axis is labeled from negative 6 to 6 in increments of 2, and the y-axis is labeled from negative 6 to 6 in increments of 2. Point z is plotted at (negative 3 comma negative 5). Point z times i is plotted at (negative 3 comma 5).
D
Image with description Complex plane with the horizontal axis labeled real and the vertical axis labeled imaginary. The x-axis is labeled from negative 6 to 6 in increments of 2, and the y-axis is labeled from negative 6 to 6 in increments of 2. Point z is plotted at (negative 3 comma negative 5). Point z times i is plotted at (5 comma negative 3).
3

What is the product of open paren 3 plus 5 i close paren and open paren 2 minus 6 i close paren ?

A
6 minus 30 i
B
negative 24 minus 8 i
C
negative 24 minus 28 i
D
36 minus 8 i
4

Let z is equal to 0 point 3 times open paren cosine of open paren 31 degrees close paren plus i sine open paren 31 degrees close paren close paren and w is equal to 20 times open paren cosine of open paren 18 degrees close paren plus i sine open paren 18 degrees close paren close paren Which statement describes the geometric construction of the product z w on the complex plane?

A
Stretch z by a factor of 20 , then rotate 49 degrees counterclockwise.
B
Stretch z by a factor of 6 , then rotate 49 degrees counterclockwise.
C
Stretch z by a factor of 6 , then rotate 18 degrees counterclockwise.
D
Stretch z by a factor of 20 , then rotate 18 degrees counterclockwise.
5

What is the product of 16 times open paren cosine of open paren 47 degrees close paren plus i sine open paren 47 degrees close paren close paren and 4 times open paren cosine of open paren 12 degrees close paren plus i sine open paren 12 degrees close paren close paren ?

A
64 times open paren cosine of open paren 35 degrees close paren plus i sine open paren 35 degrees close paren close paren
B
20 times open paren cosine of open paren 59 degrees close paren plus i sine open paren 59 degrees close paren close paren
C
20 times open paren cosine of open paren 35 degrees close paren plus i sine open paren 35 degrees close paren close paren
D
64 times open paren cosine of open paren 59 degrees close paren plus i sine open paren 59 degrees close paren close paren
6

Which statement describes how to geometrically divide a complex number, z , by a second complex number, w ?

A
Scale z by the modulus of w , then rotate counterclockwise by the argument of w .
B
Scale z by the modulus of w , then rotate clockwise by the argument of w .
C
Scale z by the reciprocal of the modulus of w , then rotate counterclockwise by the argument of w .
D
Scale z by the reciprocal of the modulus of w , then rotate clockwise by the argument of w .
7

For z is equal to negative 2 plus 2 i , which graph represents z and negative 2 z ?

A
Image with description A coordinate plane with a horizontal axis labeled real and a vertical axis labeled imaginary. The axes are labeled from negative 6 to 6 in increments of 2 with grid lines every 1 unit. A point labeled z is plotted at negative 2 comma 2. A point labeled negative 2 z is plotted at negative 1 comma negative 1.
B
Image with description A coordinate plane with a horizontal axis labeled real and a vertical axis labeled imaginary. The axes are labeled from negative 6 to 6 in increments of 2 with grid lines every 1 unit. A point labeled z is plotted at negative 2 comma 2. A point labeled negative 2 z is plotted at 4 comma negative 4.
C
Image with description A coordinate plane with a horizontal axis labeled real and a vertical axis labeled imaginary. The axes are labeled from negative 6 to 6 in increments of 2 with grid lines every 1 unit. A point labeled z is plotted at negative 2 comma 2. A point labeled negative 2 z is plotted at 1 comma negative 1.
D
Image with description A coordinate plane with a horizontal axis labeled real and a vertical axis labeled imaginary. The axes are labeled from negative 6 to 6 in increments of 2 with grid lines every 1 unit. A point labeled z is plotted at negative 2 comma 2. A point labeled negative 2 z is plotted at negative 4 comma negative 4.

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Multiply and Divide Complex Numbers — Quiz…