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.