Question

in the number $7 + 3i$, what type of number is $3i$? (1 point)

$\bigcirc$ rational

$\bigcirc$ real

$\bigcirc$ irrational

$\bigcirc$ imaginary

Explanation:

An imaginary number is defined as a number of the form \(bi\) where \(b\) is a real number and \(i = \sqrt{- 1}\). In the complex number \(7 + 3i\), the term \(3i\) is of the form \(bi\) (with \(b = 3\)) and thus is an imaginary number. Rational numbers are real numbers that can be expressed as a fraction of two integers, real numbers are numbers that can be represented on the number line, and irrational numbers are real numbers that cannot be expressed as a fraction of two integers. Since \(3i\) involves the imaginary unit \(i\), it is not a real, rational, or irrational number.

Answer:

D. imaginary (assuming the options are labeled A. rational, B. real, C. irrational, D. imaginary; if the last option is "imaginary" as per the given choices, the correct option is the one with "imaginary", e.g., if the options are in order as given: the fourth option (the one with "imaginary")).