QuestionAugust 25, 2025

Write in terms of i. Simplify your answer as much as possible. -sqrt (-4) square

Write in terms of i. Simplify your answer as much as possible. -sqrt (-4) square
Write in terms of i. Simplify your answer as much as possible. -sqrt (-4) square

Solution
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Answer

-2i Explanation 1. Simplify the expression inside the square root -\sqrt{-4} can be rewritten as -\sqrt{4 \cdot (-1)}. 2. Apply the property of square roots \sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}. So, -\sqrt{4 \cdot (-1)} = -\sqrt{4} \cdot \sqrt{-1}. 3. Calculate the square roots \sqrt{4} = 2 and \sqrt{-1} = i. 4. Multiply the results -2 \cdot i = -2i.

Explanation

1. Simplify the expression inside the square root<br /> $-\sqrt{-4}$ can be rewritten as $-\sqrt{4 \cdot (-1)}$.<br />2. Apply the property of square roots<br /> $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$. So, $-\sqrt{4 \cdot (-1)} = -\sqrt{4} \cdot \sqrt{-1}$.<br />3. Calculate the square roots<br /> $\sqrt{4} = 2$ and $\sqrt{-1} = i$.<br />4. Multiply the results<br /> $-2 \cdot i = -2i$.
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