Question 1

Which of the following is the correct simplification of $$\sqrt{700}$$?

Accepted Answer

$$10\sqrt{7}$$

Question 2

What is the definition of the imaginary unit $$i$$?

Accepted Answer

$$i = \sqrt{-1}$$

Question 3

Simplify $$\sqrt{50x^4$y^3$$}$ as much as possible.

Accepted Answer

$$5x^2y$$\sqrt{2y}$$

Question 4

Which of the following is the correct way to rationalize the denominator of $$\frac{\sqrt{7}}{\sqrt{5}}$$?

Accepted Answer

$$\frac{\sqrt{35}}{5}$$

Question 5

What is $$i^7$$ equal to?

Accepted Answer

$$-i$$

Question 6

If $$x^2 + 1 = 0$, what are the solutions for x$?

Accepted Answer

$$x = \pm i$$

Question 7

Which of the following best describes the cycle of powers of $$i$$?

Accepted Answer

The powers of $$i$$ repeat every 4 terms.

Question 8

Simplify $$\sqrt{32}.$$

Accepted Answer

$$4\sqrt{2}$$

Question 9

Which of the following is the standard form of a complex number?

Accepted Answer

$$a + bi$$

Question 10

What is the value of $$i^{2023}$$?

Accepted Answer

$$-i$$

Question 11

Which of the following is the correct simplification of $$\sqrt{-49}$$?

Accepted Answer

$$7i$$

Question 12

If $$z = 3 + 4i$$, what is the complex conjugate of $$z$$?

Accepted Answer

$$3 - 4i$$

Question 13

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

Accepted Answer

$$5 + 3i$$

Question 14

Simplify $$\sqrt{18x^2$}.$$

Accepted Answer

$$3x\sqrt{2}$$

Question 15

Which of the following is the correct simplification of $$\sqrt{-12}$$?

Accepted Answer

$$2i\sqrt{3}$$

Question 16

If $$a = 5$$ and $$b = -2$$, what is the standard form of the complex number $$a + bi$$?

Accepted Answer

$$5 - 2i$$

Question 17

What is the result of multiplying $$(2 + 3i) by$$ $$(1 - i)$$?

Accepted Answer

$$5 + i$$

Question 18

Which of the following is the correct simplification of $$\sqrt{75}$$?

Accepted Answer

$$5\sqrt{3}$$

Question 19

If $$i^2 = -1$, what is i^4$?

Accepted Answer

$$1$$

Question 20

Which of the following is the correct simplification of $$\sqrt{8x^3$}$$?

Accepted Answer

$$2x\sqrt{2x}$$

Radical Expressions and Complex Numbers: Study Notes for College Algebra

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