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

1. Recall the definitions: A real number is any number that can be found on the number line, including zero, positive, and negative numbers.
2. A complex number is any number that can be written in the form \(a + bi\), where \(a\) and \(b\) are real numbers and \(i\) is the imaginary unit with \(i^2 = -1\).
3. A pure imaginary number is a complex number where the real part \(a = 0\) and the imaginary part \(b \neq 0\).
4. A nonreal complex number is a complex number where the imaginary part \(b \neq 0\), meaning it is not purely real.
5. Since the number given is \$0\(, it can be written as \)0 + 0i$, which means it is a real number and also a complex number, but it is neither pure imaginary nor nonreal complex.

Key Concepts

Real Numbers

Real numbers include all the numbers that can be found on the number line, including zero, positive and negative integers, fractions, and irrational numbers. They do not have an imaginary component and are used to measure continuous quantities.

Complex Numbers

Complex numbers consist of a real part and an imaginary part and are expressed in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit with the property i² = -1. All real numbers are also complex numbers with zero imaginary part.

Pure Imaginary Numbers

Pure imaginary numbers are complex numbers where the real part is zero and the imaginary part is nonzero, written as 0 + bi (b ≠ 0). They lie on the imaginary axis of the complex plane and are distinct from real numbers.