Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptions will apply.) -6 -2i

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. In the context of the question, -6 is a real number because it is a whole number that lies on the number line.

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 'b' is the coefficient of the imaginary unit 'i'. The imaginary unit 'i' is defined as the square root of -1. In the question, -2i is a complex number where the real part is 0 and the imaginary part is -2.

Imaginary Numbers

Imaginary numbers are a subset of complex numbers where the real part is zero, and they are expressed in the form bi, where 'b' is a real number. These numbers cannot be represented on the traditional number line. In the question, -2i is classified as a pure imaginary number because it has no real component, only an imaginary one.