Question

To which set(s) of numbers does the number sqrt -16 belong? Select all that apply.

real numbers
complex numbers***
rational numbers
imaginary numbers***
irrational numbers

I can only pick two, and that's what I think it is. Please check? Thanks

Answer 1

1. Real numbers.
2. Complex numbers.
3. Rational numbers.
4. Imaginary numbers.
5. Irrational numbers.

Answer 2

The square root of -16 is an imaginary number and a complex number. Sqrt(-16)=4i. We use the i to indicate that the number is imaginary since there is no number that can be multiplied by itself to get a negative number (a negative times a negative is a positive, and a positive times a positive is also a positive). So the use of i tells you immediately that it's an imaginary number. You can tell the number is complex because it has both a real and an imaginary part and could be written in the form a+bi, where a is a real number and bi is an imaginary number. In this specific case, the real part (a) is 0 and the imaginary part (bi) is 4i.