Question 1

Simplify the expression and write your answer in the standard form $$a + bi$$: $$(4 + 2i) + (7 - 5i).$$

Accepted Answer

$$11 - 3i$$

Question 2

Which of the following is the correct result of $$(6 - 8i) - (2 + 3i) in $$standard form?

Accepted Answer

$$4 - 11i$$

Question 3

A medical imaging device uses the complex number $$z = 5 + 12i to $$represent a signal. What is the modulus (absolute value) of $$z$$?

Accepted Answer

$$13$$

Question 4

Which of the following is the result of multiplying $$(2 + 3i)$$ and $$(4 - i)$$?

Accepted Answer

$$11 + 10i$$

Question 5

A chemical reaction is modeled by the complex number $$z = 7 - 2i. $$What is the conjugate of $$z$$?

Accepted Answer

$$7 + 2i$$

Question 6

Divide the complex numbers and write the answer in standard form: $$\dfrac{3 + 4i}{1 - 2i}.$$

Accepted Answer

$$-1 + 2i$$

Question 7

Which of the following is the result of $$(5 + 6i) - (3 - 2i)$$?

Accepted Answer

$$2 + 8i$$

Question 8

If $$z = 2 - 5i$$, what is $$z^*$$, the complex conjugate of $$z$$?

Accepted Answer

$$2 + 5i$$

Question 9

A signal in an electrical circuit is represented by $$z = -3 + 4i. $$What is the modulus of $$z$$?

Accepted Answer

$$5$$

Question 10

Which of the following is the result of multiplying $$(1 - 3i)$$ and $$(8 + 7i)$$?

Accepted Answer

$$29 - 17i$$

Question 11

A physicist uses the complex number $$z = 6 + 8i in a $$calculation. What is the modulus of $$z$$?

Accepted Answer

$$10$$

Question 12

Simplify the expression: $$(7 + 2i) + (-3 + 5i).$$

Accepted Answer

$$4 + 7i$$

Question 13

Which of the following is the result of dividing $$4 + 2i by$$ $$2 - i$$?

Accepted Answer

$$2 + 2i$$

Question 14

A biologist models population growth using $$z = 3 + 7i. $$What is the conjugate of $$z$$?

Accepted Answer

$$3 - 7i$$

Question 15

Simplify $$(2 - 3i) + (5 + 4i).$$

Accepted Answer

$$7 + i$$

Question 16

Which of the following is the result of $$(6 + 2i) - (4 + 7i)$$?

Accepted Answer

$$2 - 5i$$

Question 17

A signal in a communications system is represented by $$z = 9 - 12i. $$What is the modulus of $$z$$?

Accepted Answer

$$15$$

Question 18

Which of the following is the result of multiplying $$(3 + 2i)$$ and $$(5 - 4i)$$?

Accepted Answer

$$23 - 2i$$

Question 19

Simplify $$(8 - 5i) + (2 + 9i).$$

Accepted Answer

$$10 + 4i$$

Question 20

Which of the following is the result of dividing $$5 + 3i by$$ $$1 + i$$?

Accepted Answer

$$4 + i$$

Complex Numbers: Standard Form and Operations

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