AnswersMath 4Complex Numbers

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1
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Given a pair of complex numbers, z sub 1 is equal to 5 and z sub 2 is equal to negative 6 i , let z sub 3 is equal to 3 i plus z sub 1 and z sub 4 is equal to z sub 2 minus 2 In which quadrant is z sub 3 minus z sub 4 located?

A
quadrant II
B
quadrant III
C
quadrant IV
D
quadrant I
2
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Which phrase describes how to divide a complex number z by r times open paren cosine theta plus i sine theta close paren ?

A
Scale by a factor of 1 over r and rotate clockwise by theta .
B
Scale by a factor of r and rotate counterclockwise by theta .
C
Scale by a factor of 1 over r and rotate counterclockwise by theta .
D
Scale by a factor of r and rotate clockwise by theta .
3

Which property of multiplication is shown here? If x is equal to 3 plus 4 i and y is equal to 5 plus 6 i , x times y is equal to y times x

A
commutative property
B
identity property
C
associative property
D
distributive property
4

Which expression is equivalent to open paren 3 plus 5 i close paren squared ?

A
negative 16 plus 30 i
B
6 plus 34 i
C
negative 16 minus 34 i
D
16 plus 30 i
5

For two complex numbers z and w , which diagram shows the geometric representation of z w ?

A
Image with description A graph has a horizontal axis labeled real and a vertical axis labeled imaginary. Three rays originate from the origin, ordered counter-clockwise from lowest to highest angle. The lowest ray extends to a point labeled w, with a length labeled r 2 and an angle from the horizontal axis labeled theta 2. The middle ray extends to a point labeled z, with a length labeled r 1 and an angle from the horizontal axis labeled theta 1. The highest ray extends to a point labeled z w, with a length labeled r 1 r 2 and an overall angle from the horizontal axis labeled theta 1 + theta 2.
B
Image with description A graph has a horizontal axis labeled real and a vertical axis labeled imaginary. Three rays originate from the origin, ordered counter-clockwise from lowest to highest angle. The lowest ray extends to a point labeled w, with a length labeled r 2 and an angle from the horizontal axis labeled theta 2. The middle ray extends to a point labeled z w, with a length labeled r 1 r 2 and an angle from the horizontal axis labeled theta 1 minus theta 2. The highest ray extends to a point labeled z, with a length labeled r 1 and an angle from the horizontal axis labeled theta 1.
C
Image with description A graph has a horizontal axis labeled real and a vertical axis labeled imaginary. Three rays originate from the origin, ordered counter-clockwise from lowest to highest angle. The lowest ray extends to a point labeled w, with a length labeled r 2 and an angle from the horizontal axis labeled theta 2. The middle ray extends to a point labeled z, with a length labeled r 1 and an angle from the horizontal axis labeled theta 1. The highest ray extends to a point labeled z w, with a length labeled r 1 + r 2 and an overall angle from the horizontal axis labeled theta 1 + theta 2.
D
Image with description A graph has a horizontal axis labeled real and a vertical axis labeled imaginary. Three rays originate from the origin, ordered counter-clockwise from lowest to highest angle. The lowest ray extends to a point labeled w, with a length labeled r 2 and an angle from the horizontal axis labeled theta 2. The middle ray extends to a point labeled z w, with a length labeled r 1 + r 2 and an angle from the horizontal axis labeled theta 1 minus theta 2. The highest ray extends to a point labeled z, with a length labeled r 1 and an angle from the horizontal axis labeled theta 1.
6

Which process would produce the complex number w sub 2 ?

A
Subtract 3 minus i from w sub 1 .
B
Add 3 minus i to w sub 1 .
C
Subtract negative 9 plus 3 i from w sub 1 .
D
Add negative 9 plus 3 i to w sub 1 .

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