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

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College Algebra

1. Equations & Inequalities

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0:32 minutes

Problem 12

Textbook Question

Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptions will apply.) 0

Verified step by step guidance

Step 1: Understand the types of numbers involved. Real numbers include all the numbers on the number line, complex numbers are of the form a + bi where a and b are real numbers, and pure imaginary numbers are of the form 0 + bi.

Step 2: Recognize that the number 0 can be expressed as 0 + 0i, which fits the form of a complex number where both the real part (a) and the imaginary part (b) are zero.

Step 3: Since 0 can be expressed as 0 + 0i, it is a complex number.

Step 4: The number 0 is also a real number because it is located on the real number line.

Step 5: Conclude that the number 0 is both a real number and a complex number.

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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, 'b' is the coefficient of the imaginary unit 'i' (where i² = -1). They extend the concept of one-dimensional number lines to two dimensions, allowing for solutions to equations that have no real solutions.

Imaginary Numbers

Imaginary numbers are defined as multiples of the imaginary unit 'i', which is the square root of -1. A pure imaginary number has no real part and is expressed as bi, where b is a real number. For example, 3i is a pure imaginary number, while 0 can be considered both real and imaginary since it can be expressed as 0 + 0i.