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The expression you provided is the square root of a negative number, \( \sqrt{-3.24} \).

In the real number system, there is no real number whose square is negative, so this expression does not have a real number solution. However, in the system of complex numbers, the square root of a negative number can be expressed in terms of imaginary numbers.

We can rewrite the expression as:

\[
\sqrt{-3.24} = \sqrt{-1} \times \sqrt{3.24} = i \times \sqrt{3.24}
\]

Since \( \sqrt{3.24} = 1.8 \), we have:

\[
\sqrt{-3.24} = 1.8i
\]

Thus, the solution in the complex number system is \( 1.8i \).

Would you like more details or have any other questions?

Here are 5 related questions to explore this topic further:

1. What are imaginary numbers, and how are they used in mathematics?
2. Can all negative square roots be expressed as complex numbers?
3. How do we add and multiply complex numbers?
4. What is the significance of the imaginary unit \(i\) in various fields of science?
5. How do we find the square root of a complex number?

**Tip**: The imaginary unit \(i\) is defined as the square root of \(-1\), and it's used extensively in engineering, physics, and other fields to handle problems involving oscillations, waves, and more.

Explore how to find the square root of a negative number like √-3.24 using complex numbers. This solution involves understanding imaginary numbers, where √-1 = i, and expressing the result in terms of i. Suitable for high school students learning about complex numbers.

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