What is the square root of -4

General
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what is the square root of -4

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What is the square root of -4?

Answer: To determine the square root of -4, we need to explore the concept of imaginary numbers. The square root of a negative number isn’t a real number; it lies within the realm of complex numbers.

  1. Understanding Imaginary Unit (i):

    • The imaginary unit (i) is defined as the square root of -1.
    • That is, (i = \sqrt{-1}).

  2. Breaking Down the Square Root:

    • Given (-4), we can rewrite it in terms of (i).
    • (\sqrt{-4}) can be rewritten as (\sqrt{4 \cdot -1}).

  3. Simplification Process:

    • Separate the product under the square root: (\sqrt{4} \cdot \sqrt{-1}).
    • Recall that (\sqrt{4} = 2) and (\sqrt{-1} = i).

  4. Combining the Results:

    • Therefore, (\sqrt{-4} = 2i).

Verification:

To ensure the result is accurate, let’s square our solution:

(2i)^2 = 2^2 \cdot i^2 = 4 \cdot (-1) = -4

Thus, when you square (2i), you indeed get (-4), confirming the calculation is correct.

Conclusion:

The square root of (-4) is (\boxed{2i}). This belongs to the set of complex numbers because it involves the imaginary unit (i).