Question 1

Which of the following is the correct definition of the imaginary unit $$i$$?

Accepted Answer

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

Question 2

Given the complex numbers $$z_1 = 4 - 3i$ and z_2$ = 2 + 5i$$, what is $$z_1$$ + $$z_2$$?

Accepted Answer

$$6 + 2i$$

Question 3

Which of the following is the complex conjugate of $$7 - 2i$$?

Accepted Answer

$$7 + 2i$$

Question 4

If $$z = 3 + 4i$$, what is $$z \cdot \overline{z}$$, where $$\overline{z} is $$the complex conjugate of $$z$$?

Accepted Answer

$$25$$

Question 5

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

Accepted Answer

$$13$$

Question 6

What is the result of $$(2 + 3i)(4 - i)$$?

Accepted Answer

$$11 + 10i$$

Question 7

A chemical reaction is modeled by the equation $$x^2 + 6x + 13 = 0$. What are the solutions?

Accepted Answer

$$x = -3 \pm 2i$$

Question 8

Which of the following is a pure imaginary number?

Accepted Answer

$$5i$$

Question 9

What is the principal square root of $$-49$$?

Accepted Answer

$$7i$$

Question 10

A signal in an electrical circuit is represented by $$z = -6 + 8i. $$What is the sum of the real and imaginary parts?

Accepted Answer

$$2$$

Question 11

Divide $$3 + 2i by$$ $$1 - i$$ and write the result in standard form.

Accepted Answer

$$\frac{5}{2} + \frac{1}{2}i$$

Question 12

Which operation is necessary to divide complex numbers and obtain a real denominator?

Accepted Answer

Multiply numerator and denominator by the complex conjugate of the denominator

Question 13

If $$z_1 = 2 - 5i$ and z_2$ = 3 + 4i$$, what is $$z_1$$ - $$z_2$$?

Accepted Answer

$$-1 - 9i$$

Question 14

A quadratic equation $$x^2 + 4x + 8 = 0$ models the population growth in a lab experiment. What are its solutions?

Accepted Answer

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

Question 15

Which of the following statements is true about the product of a complex number and its conjugate?

Accepted Answer

The product is always a real number

Question 16

What is the result of $$(-3 + 2i) + (5 - 7i)$$?

Accepted Answer

$$2 - 5i$$

Question 17

A physicist uses the complex number $$z = 6i in a $$calculation. What is the real part of $$z$$?

Accepted Answer

$$0$$

Question 18

What is the result of $$(1 + 2i)(3 - 4i)$$?

Accepted Answer

$$11 - 2i$$

Question 19

Which of the following is NOT a complex number?

Accepted Answer

$$\infty$$

Question 20

If $$z = a + bi$$ and $$a = 0$$, $$b 
eq 0$$, what type of number is $$z$$?

Accepted Answer

Pure imaginary number

Complex Numbers in Precalculus: Operations and Applications

Study Guide - Practice Questions