AnswersAlgebra 2Performing Operations with Complex Numbers

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1
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Which equation is an example of the commutative property of multiplication?

A
open paren 8 plus 6 i close paren is equal to open paren 6 i plus 8 close paren
B
open paren 8 plus 6 i close paren times open paren 7 minus 9 i close paren is equal to open paren 7 minus 9 i close paren times open paren 8 plus 6 i close paren
C
open paren 8 plus 6 i close paren times open paren 7 minus 9 i close paren is equal to open paren 8 plus 6 i close paren times open paren 7 minus 9 i close paren times 1
D
open paren 8 plus 6 i close paren is equal to open paren 8 plus 6 i plus 0 close paren
2
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What is the additive inverse of the complex number 13 minus 2 i ?

A
negative 13 minus 2 i
B
13 plus 2 i
C
13 minus 2 i
D
negative 13 plus 2 i
3

Which equation shows an example of the associative property of addition?

A
open paren negative 7 plus i close paren plus 7 i is equal to negative 7 plus open paren i plus 7 i close paren
B
open paren negative 7 plus i close paren plus 7 i is equal to 7 i plus open paren negative 7 i plus i close paren
C
open paren negative 7 i plus i close paren plus 0 is equal to open paren negative 7 i plus i close paren
D
7 i times open paren negative 7 i plus i close paren is equal to open paren 7 i minus 7 i close paren plus open paren 7 i times i close paren
5

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression open paren negative 3 plus i close paren plus open paren 18 plus 5 i close paren ?

A
negative open paren 3 minus i close paren plus open paren 18 plus 5 i close paren
B
negative 3 plus open paren i plus 18 close paren plus 5 i
C
open paren negative 3 plus i close paren plus open paren 18 plus 5 i close paren plus 0
D
open paren negative 3 plus 18 close paren plus open paren i plus 5 i close paren
6

Which property of addition is shown here? 3 plus 4 i plus 5 plus 6 i is equal to 3 plus 5 plus 4 i plus 6 i

A
inverse property
B
commutative property
C
associative property
D
identity property
7

Which property of addition is shown in the equation? c plus d i plus 0 plus 0 i is equal to c plus d i

A
identity property
B
associative property
C
inverse property
D
commutative property
9

Helene is finding the sum open paren 9 plus 10 i close paren plus open paren negative 8 plus 11 i close paren She rewrites the sum as open paren negative 8 plus 11 close paren times i plus open paren 9 plus 10 close paren times i Which statement explains the property of addition that she made an error in using?

A
Helene incorrectly used the identity property by combining the real number and the coefficient of the imaginary part.
B
Helene incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.
C
Helene incorrectly used the associative property by changing the order of the two complex numbers.
D
Helene incorrectly used the commutative property by changing the order of the two complex numbers.
10

Which equation illustrates the identity property of multiplication?

A
open paren x plus y i close paren times open paren z plus w i close paren is equal to open paren z plus w i close paren times open paren x plus y i close paren
B
open paren x plus y i close paren times 0 is equal to 0
C
open paren x plus y i close paren times z is equal to open paren x z plus y z i close paren
D
open paren x plus y i close paren times 1 is equal to open paren x plus y i close paren

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