Question

express in terms of \\(i\\).

\\(\sqrt{-16}\\)

\\(\sqrt{-16} = \square\\)
(simplify your answer. type your answer in the form \\(a + bi\\).)

Explanation:

Define the imaginary unit

We define the imaginary unit \(i\) to represent the square root of \(-1\):

$$i = \sqrt{-1}$$

Apply radical properties

Using the Product Rule for Radicals and Square Root Properties knowledge points

$$\sqrt{-16} = \sqrt{16 \cdot (-1)} = \sqrt{16} \cdot \sqrt{-1}$$

Simplify the expression

Using the Square Root Properties knowledge point

$$\sqrt{16} \cdot \sqrt{-1} = 4 \cdot i = 4i$$

Write in standard complex form

The standard form of a complex number is \(a + bi\), where \(a\) is the real part and \(b\) is the imaginary part. Since there is no real part, we write:

$$0 + 4i$$

Answer:

\(\sqrt{-16} =\) <blank>\(0 + 4i\)</blank>
(Simplify your answer. Type your answer in the form a + bi.)