The expression \(\sqrt{-16}\) involves finding the square root of a negative number, which leads us to the concept of imaginary numbers.

We cannot find the square root of a negative number using real numbers. However, we define the imaginary unit \(i\), where:

\[
i = \sqrt{-1}
\]

Using this definition, we can rewrite \(\sqrt{-16}\) as:

\[
\sqrt{-16} = \sqrt{16} \times \sqrt{-1} = 4i
\]

So, \(\sqrt{-16} = 4i\).

Would you like more details or have any questions?

Here are 5 related questions:
1. What is \(\sqrt{-25}\)?
2. How do we handle higher powers of \(i\)?
3. What is \( (4i)^2 \)?
4. How do imaginary numbers apply in solving quadratic equations?
5. What is the general form of a complex number?

**Tip:** Imaginary numbers are essential when dealing with equations that don't have real-number solutions, especially in fields like engineering and physics.

Discover how to solve \(\sqrt{-16}\) by introducing imaginary numbers. Learn the concept of the imaginary unit \(i = \sqrt{-1}\) and see how this helps in calculating \(\sqrt{-16} = 4i\). Suitable for students in Grades 9-12 learning about complex numbers.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation