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The image asks for the square roots of \(-4\).

The square root of a negative number involves complex numbers, since no real number squared gives a negative result. To express the square root of \(-4\), we use the imaginary unit \(i\), where \(i^2 = -1\).

The solution is:

\[
\sqrt{-4} = \sqrt{4 \times (-1)} = \sqrt{4} \times \sqrt{-1} = 2i
\]

Thus, the square roots of \(-4\) are:
\[
\pm 2i
\]

Would you like further details or have any questions?

Here are five related questions you might find useful:
1. What are the square roots of other negative numbers like \(-9\) or \(-16\)?
2. How do we define complex numbers in general?
3. What is the geometric interpretation of complex numbers on the complex plane?
4. How do you add, subtract, and multiply complex numbers?
5. What is the significance of imaginary numbers in physics or engineering?

**Tip:** The square root of a negative number always involves an imaginary number, denoted by \(i\), where \(i^2 = -1\).

Explore the square roots of -4 and how imaginary numbers are used to represent solutions for negative square roots. This guide explains key algebraic concepts like complex numbers and imaginary unit i, providing a step-by-step solution for √(-4) = ±2i.

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