Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptions will apply.) -7i

검증된 단계별 안내

Recognize that the number given is \(-7i\), where \(i\) is the imaginary unit defined by \(i^2 = -1\).

Recall the definitions: a real number has no imaginary part, a complex number is of the form \(a + bi\) where \(a\) and \(b\) are real numbers, a pure imaginary number has zero real part and a nonzero imaginary part, and a nonreal complex number is a complex number with a nonzero imaginary part and zero or nonzero real part but not purely real.

Identify the real part (\(a\)) and the imaginary part (\(b\)) of the number \(-7i\). Here, \(a = 0\) and \(b = -7\).

Since \(a = 0\) and \(b eq 0\), the number \(-7i\) is a pure imaginary number.

Because every pure imaginary number is also a complex number, \(-7i\) is both pure imaginary and complex, but not real.

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주요 개념

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Real and Complex Numbers

Real numbers include all rational and irrational numbers that can be found on the number line. Complex numbers consist of a real part and an imaginary part, expressed as a + bi, where a and b are real numbers and i is the imaginary unit with i² = -1.

Imaginary and Pure Imaginary Numbers

Imaginary numbers are multiples of the imaginary unit i. A pure imaginary number has no real part and is written as bi, where b is a nonzero real number. For example, -7i is pure imaginary because its real part is zero.

Nonreal Complex Numbers

Nonreal complex numbers are complex numbers whose real part is zero or nonzero but have a nonzero imaginary part, making them not purely real. Pure imaginary numbers are a subset of nonreal complex numbers since their real part is zero but imaginary part is nonzero.