Question

what type of number is $-296.2i$?
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 \(-296.2i\) has the imaginary unit \(i\), it is not a real number, so option A is incorrect.
• An imaginary number is defined as a number of the form \(bi\) where \(b\) is a real number and \(b

eq0\) (when \(b = 0\), the number is \(0\) which is a real number). Here, \(-296.2i\) is in the form \(bi\) with \(b=- 296.2
eq0\), so it is an imaginary number, option B is correct.

• A complex number is defined as a number of the form \(a + bi\) where \(a\) and \(b\) are real numbers. For \(-296.2i\), we can write it as \(0+(- 296.2)i\), where \(a = 0\) and \(b=-296.2\) are real numbers. So all imaginary numbers are also complex numbers (since they can be written in the form \(a + bi\) with \(a = 0\)), so option C is correct.

Answer:

B. Imaginary, C. Complex