express the square root of -81 as a complex number

The square root of \(-81\) involves an imaginary number because the square root of a negative number isn't a real number. To express this, we use the imaginary unit \(i\), where \(i = \sqrt{-1}\).

\[
\sqrt{-81} = \sqrt{-1 \times 81} = \sqrt{-1} \times \sqrt{81} = i \times 9 = 9i
\]

So, the square root of \(-81\) is \(9i\), where \(i\) is the imaginary unit.

Would you like more details or have any questions?

Here are 5 related questions to explore this concept further:

1. What are the basic properties of imaginary numbers?
2. How do you add and subtract complex numbers?
3. How do you multiply and divide complex numbers?
4. How do you solve quadratic equations that involve complex numbers?
5. What is the geometric interpretation of complex numbers on the complex plane?

**Tip**: When dealing with complex numbers, remember that \(i^2 = -1\), which is essential for simplifying expressions.

Express the square root of -81 as a complex number.

Learn how to express the square root of -81 as a complex number using the imaginary unit. This solution explores key concepts such as imaginary numbers and complex numbers, suitable for students in Grades 9-10.

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