The expression \( \sqrt{-144} \) involves taking the square root of a negative number, which isn't possible in the realm of real numbers. However, in the field of complex numbers, we use the imaginary unit \( i \), where \( i = \sqrt{-1} \).

Thus, we can rewrite:

\[
\sqrt{-144} = \sqrt{144} \times \sqrt{-1} = 12i
\]

So, \( \sqrt{-144} = 12i \) in the complex number system.

Would you like any additional details or have any further questions?

Here are five related questions to expand on this topic:
1. What is the definition of an imaginary number?
2. How do you simplify \( \sqrt{-x} \) for any positive value of \( x \)?
3. What is the value of \( i^2 \), and how does it affect calculations involving \( i \)?
4. How do you add and subtract complex numbers?
5. Can you explain how the quadratic formula works with complex roots?

**Tip:** Always express square roots of negative numbers in terms of \( i \) to work within the complex number system.

Learn how to solve \\sqrt{-144} by using complex numbers and the imaginary unit i. This problem covers key concepts in complex numbers, including simplifying square roots of negative numbers. Suitable for students in Grades 10-12.

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