Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Complex Numbers

College Algebra

1. Equations & Inequalities

Complex Numbers

Previous problemNext problem

0:49 minutes

Problem 18

Textbook Question

Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptions will apply.) √24

Verified step by step guidance

Step 1: Recognize that \( \sqrt{24} \) is a square root of a positive number.

Step 2: Understand that the square root of any positive number is a real number.

Step 3: Simplify \( \sqrt{24} \) by expressing it as \( \sqrt{4 \times 6} \).

Step 4: Further simplify to \( 2\sqrt{6} \), which is still a real number.

Step 5: Conclude that \( \sqrt{24} \) is a real number and not a complex or pure imaginary number.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

49s

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Real Numbers

Real numbers include all the numbers that can be found on the number line, encompassing both rational numbers (like integers and fractions) and irrational numbers (like √2 and π). They can be positive, negative, or zero, and they do not involve imaginary components.

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where 'a' is the real part and 'bi' is the imaginary part. The imaginary unit 'i' is defined as the square root of -1, allowing for the representation of numbers that cannot be found on the real number line.

Imaginary Numbers

Imaginary numbers are a subset of complex numbers where the real part is zero, and they are expressed in the form bi. A pure imaginary number is specifically of the form bi, where 'b' is a real number. For example, √-1 is an imaginary number, while √24 is a real number that can be simplified to 2√6.