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

Key Concepts

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.