Question

Express the radical using the imaginary unit, i.

Express your answer in simplified form.
± s√ (-9) = ± ( )

Answer 1

To express ± √(-9) using the imaginary unit i, we need to find the square root of -9. Using the properties of the imaginary unit, i, we know that i² = -1. Therefore, we can rewrite -9 as 9*(-1) and take the square root: ± √(-9) = ± √(9*(-1)) = ± √(9)*√(-1) = ± 3i. So, the answer is ± 3i.

Step-by-step explanation:

To express ± √(-9) using the imaginary unit i, we need to find the square root of -9.

Using the properties of the imaginary unit, i, we know that i² = -1. Therefore, we can rewrite -9 as 9*(-1) and take the square root:

± √(-9) = ± √(9*(-1)) = ± √(9)*√(-1) = ± 3i

So, the answer is ± 3i.

Expressing the radical using the imaginary unit i simplifies the expression ± √ (-9). The number -9 under the square root is a negative number, and the square root of a negative number involves the imaginary unit i, which is defined as √(-1). To simplify √(-9), we can rewrite it as √(9) √(-1).

Since the square root of 9 is 3, and the square root of -1 is i, the simplified form of the expression is ± 3i.