Question

what type of number is 15.301i? choose all answers that apply: a real b imaginary c complex

Explanation:

• A real number is a number that can be represented on the number line and does not involve the imaginary unit \(i\). Since \(15.301i\) has \(i\) (where \(i = \sqrt{- 1}\)), it is not a real number, so option A is incorrect.
• An imaginary number is a number of the form \(bi\) where \(b\) is a real number and \(b

eq0\). Here, \(15.301i\) is in the form \(bi\) with \(b = 15.301\) (a real number), so it is an imaginary number, so option B is correct.

• A complex number is a number of the form \(a + bi\) where \(a\) and \(b\) are real numbers. When \(a = 0\), the complex number is just \(bi\) (an imaginary number). So all imaginary numbers are also complex numbers. Since \(15.301i=0 + 15.301i\), it is a complex number, so option C is correct.

Answer:

B. Imaginary, C. Complex