Operations with Complex Numbers Answers

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1
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Which property of addition is shown in the equation below?a + bi + 0 + 0i = a + bi

A
commutative property
B
inverse property
C
identity property
D
associative property
3

Donte simplified the expression below.What mistake did Donte make?

Question illustration
A
He did not apply the distributive property correctly for 4(1 + 3i).
B
He did not distribute the subtraction sign correctly for 8 – 5i.
C
He added the real number and coefficient of i in 4(1 + 3i).
D
He added the two complex numbers instead of subtracted.
5

Aiko is finding the sum (4 + 5i) + (–3 + 7i). She rewrites the sum as (–3 + 7)i + (4 + 5)i. Which statement explains the error Aiko made by using a mathematical property incorrectly?

A
Aiko incorrectly used the commutative property by changing the order of the two complex numbers.
B
Aiko incorrectly used the associative property by changing the order of the two complex numbers.
C
Aiko incorrectly used the identity property by combining the real number and the coefficient of the imaginary part.
D
Aiko incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.
6

Which equation demonstrates the additive identity property?

A
(7 + 4 i) + (7 minus 4 i) = 14
Option A
B
(7 + 4 i) + 0 = 7 + 4 i
Option B
C
(7 + 4 i) (1) = 7 + 4 i
Option C
D
(7 + 4 i) + (negative 7 minus 4 i) = 0
Option D
10

Which property of multiplication is shown below? If x = a + bi and y = c + di, x × y = y × x.

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

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