Question 1

Which of the following best defines the imaginary unit $$i$$?

Accepted Answer

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

Question 2

Simplify the expression $$(5 + 4i)(6 - 7i)$$ and write your answer in standard form $$a + bi.$$

Accepted Answer

$$58 - 11i$$

Question 3

Evaluate $$\sqrt{-25}$$ and select the correct statement.

Accepted Answer

The expression is not a real number.

Question 4

Which of the following is the correct product of $$(-5 + i)(-5 - i)$$?

Accepted Answer

$$26$$

Question 5

Evaluate $$\sqrt{121} - \sqrt{100}.$$

Accepted Answer

$$1$$

Question 6

Which of the following is true about $$\sqrt{(-3)^2$}$$?

Accepted Answer

The expression is a real number. $$\sqrt{(-3)^2$} = 3$$

Question 7

Find the cube root: $$\sqrt[3]{-216}.$$

Accepted Answer

The expression is a real number. $$\sqrt[3]{-216} = -6$$

Question 8

Which of the following is NOT a real number?

Accepted Answer

$$\sqrt[4]{-256}$$

Question 9

Rewrite $$9^{1/2} as a $$radical and evaluate.

Accepted Answer

$$9^{1/2}$$ = \sqrt{9} = 3$$

Question 10

Evaluate $$128^{6/7}.$$

Accepted Answer

$$128^{6/7} = 64$

Question 11

Which of the following is the correct conjugate of $$a + bi$$?

Accepted Answer

$$a - bi$$

Question 12

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = f(3) = 9$$

Question 13

Which of the following statements is true about the product of complex conjugates $$(a + bi)(a - bi)$$?

Accepted Answer

The product is always a real number: $$a^2$$ + $$b^2$$

Question 14

Evaluate $$243^{1/5}.$$

Accepted Answer

$$243^{1/5} = 3$

Question 15

Which of the following is the correct way to add $$\frac{-2}{3} + \frac{3}{2}$$?

Accepted Answer

$$\frac{-2}{3} + \frac{3}{2} = \frac{-4}{6} + \frac{9}{6} = \frac{5}{6}$$

Question 16

Which rule determines if $$\sqrt[n]{-a} is a $$real number?

Accepted Answer

If $$n is $$odd and $$a is $$negative, the result is real.

Question 17

Simplify $$16^{-3/4}.$$

Accepted Answer

$$16^{-3/4}$$ = \frac{1}{8}$$

Question 18

Which of the following is the correct evaluation of $$\sqrt{169 - 25}$$?

Accepted Answer

$$\sqrt{144} = 12$$

Question 19

Which of the following is the correct evaluation of $$\sqrt[3]{64}$$?

Accepted Answer

$$\sqrt[3]{64} = 4$$

Key Concepts and Practice: Roots, Rational Exponents, and Complex Numbers

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