Question

Identify the number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions may apply). Square root -9

Answer 1

Answer:

• Complex

,

• Pure imaginary

,

• Nonreal complex

Explanation:

Given the number:

$\sqrt[]{-9}$

We want to determine if the number is real, complex, pure imaginary, or nonreal complex.

$\sqrt{-9}=\sqrt[]{-1\times9}=\sqrt[]{9}\times\sqrt[]{-1}=3i,i=\sqrt[]{-1}$

Since the root is not real, the number is therefore complex.

In addition, it has no real component, therefore, it is a pure imaginary

number.

It can also be referred to as a non-real complex number.