Question 1

Which of the following is the correct way to write $$\sqrt{-75} as $$the product of a real number and $$i$$?

Accepted Answer

$$5\sqrt{3}i$$

Question 2

Simplify $$\sqrt{-27} \cdot \sqrt{-3}.$$

Accepted Answer

$$9$$

Question 3

What is the standard form of $$(1 + 3i) + (3 + 5i)$$?

Accepted Answer

$$4 + 8i$$

Question 4

Which of the following is the solution to $$x^2 + 5x = 6$ using the zero-factor property?

Accepted Answer

$$x = -2 or$$ $$x = 3$$

Question 5

Solve $$x^2 - 4x + 1 = 0$ using the quadratic formula.

Accepted Answer

$$x = 2 \pm \sqrt{5}$$

Question 6

Which of the following is the correct simplification of $$\frac{2}{1 + i}$$?

Accepted Answer

$$1 - i$$

Question 7

If $$x = -2 + i is a $$solution to $$x^2 + 4x + 5 = 0$, what is the other solution?

Accepted Answer

$$-2 - i$$

Question 8

Which of the following is the correct standard form for $$(2 + 3i)(3 - 2i)$$?

Accepted Answer

$$12 + 5i$$

Question 9

Solve $$x^2 + 2x - 8 = 0$ by factoring.

Accepted Answer

$$x = -4 or$$ $$x = 2$$

Question 10

Which of the following is the correct simplification of $$\sqrt{-32}$$?

Accepted Answer

$$4\sqrt{2}i$$

Question 11

What is the sum $$(5 + 2i) + (3 - 3i) in $$standard form?

Accepted Answer

$$8 - i$$

Question 12

Which of the following is the correct solution to $$x^2 = 16$ using the square root property?

Accepted Answer

$$x = \pm 4$$

Question 13

What is the product $$(\sqrt{-3})(\sqrt{-12})$$?

Accepted Answer

$$6$$

Question 14

Which of the following is the correct standard form for $$(\sqrt{6} + i)(\sqrt{6} - i)$$?

Accepted Answer

$$7$$

Question 15

Solve $$x^2 + 2x + 5 = 0$ using the quadratic formula.

Accepted Answer

$$x = -1 \pm 2i$$

Complex Numbers and Quadratic Equations: Study Notes for College Algebra

Study Guide - Practice Questions