Operations with Complex Numbers

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What is the additive inverse of the complex number 9 – 4i?

b. -9 + 4i

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

a. (-4 + i) + 4i = -4 + (i + 4i)

What is the value of the product (3 – 2i)(3 + 2i)?

d. 13

What is the value of (-7 + 3i) – (2 – 6i)?

a. -9 + 9i

The relationship between voltage, E, current, I, and resistance, Z, is given by the equation E = IZ. If a circuit has a current I = 3 + 2i and a resistance Z = 2 – i, what is the voltage of the circuit?

c. 8 + i

Which property of addition is shown in the equation below?

a + bi + 0 + 0i = a + bi

c. identity property

Melissa and Tomas are playing a game with complex numbers. If Melissa has a score of 5 – 4i and Tomas has a score of 3 + 2i, what is their total score?

c. 8 – 2i

Donte simplified the expression below.

What mistake did Donte make?

a. He did not apply the distributive property correctly for 4(1 + 3i).

Which equation illustrates the identity property of multiplication?

d. (a + bi) × 1 = (a + bi)

Which property of addition is shown below?

a + bi + c + di = a + c + bi + di

c. commutative property

What is the additive inverse of the complex number -8 + 3i?

c. 8 – 3i

Aiko is finding the sum (4 + 5i) + (-3 + 7i). She rewrites the sum as (-3 + 7)i + (4 + 5)i. Which statement explains the mathematical property that she made an error using?

d. Aiko incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.

Which property of addition is shown below?

If x = a + bi and y = -a – bi, x + y = 0.

d. inverse property

Which property of multiplication is shown below?

If x = a + bi and y = c + di, x × y = y × x.

a. commutative property

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