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

$$i is $$defined as $$\sqrt{-1}$$

Question 3

What is the value of $$i^{43}$$?

Accepted Answer

$$i$$

Question 4

Which of the following is the result of $$(7 - 5i) + (-2 + i)$$?

Accepted Answer

$$5 - 4i$$

Question 5

When multiplying two complex numbers, which property must you remember?

Accepted Answer

$$i^2 = -1$

Question 6

What is the product of $$(4 - 3i)(7 + 5i)$$?

Accepted Answer

$$43 - 1i$$

Question 7

What is the definition of a complex conjugate?

Accepted Answer

If $$z = a + bi$$, its complex conjugate is $$a - bi$$

Question 8

What is the result when you multiply a complex number by its complex conjugate?

Accepted Answer

The result is a real number

Question 9

Simplify $$\sqrt{-108}.$$

Accepted Answer

$$6i\sqrt{3}$$

Question 10

Which of the following is the correct simplification of $$\sqrt{-8} + \sqrt{-18}$$?

Accepted Answer

Question 11

What is the result of $$\sqrt{-8} \cdot \sqrt{-18}$$?

Accepted Answer

$$12$$

Question 12

What is the goal when dividing two complex numbers?

Accepted Answer

To write the quotient in the form $$a + bi$$

Question 13

Simplify $$\frac{1 - 3i}{5 - 2i}$$ and write your answer in the form $$a + bi.$$

Accepted Answer

$$-0.034 + 0.586i$$

Question 14

True or False: $$\sqrt{a}\sqrt{b} = \sqrt{ab}$$ for all real numbers $$a$$ and $$b. $$Explain.

Accepted Answer

False, this property does not hold when $$a or$$ $$b is $$negative

Question 15

Which of the following is the correct simplification of $$\sqrt{50x^4$y^3$$}$?

Accepted Answer

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

Question 16

Rationalize the denominator of $$\frac{\sqrt{7}}{\sqrt{5}}.$$

Accepted Answer

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

Question 17

If $$M is a $$positive real number, which property is true for $$\sqrt{-M}$$?

Accepted Answer

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

Question 18

Which of the following is NOT a complex number?

Accepted Answer

None of the above; all are complex numbers

Question 19

Multiply the complex number $$z = -2 - 7i by $$its complex conjugate $$\overline{z} = -2 + 7i. $$What is the result?

Accepted Answer

$$53$$

Question 20

Which of the following best describes the cyclic nature of powers of $$i$$?

Accepted Answer

The powers of $$i$$ repeat every four terms: $$i, -1, -i, 1$$

1.3

Study Guide - Practice Questions