Question
\( \leftarrow \quad \begin{array}{l}\text { Express in terms of } i \text {. Save } \\ -\sqrt{-4} \\ -\sqrt{-4}=\square \\ \text { (Simplify your answer. Type your answer in the form } \mathrm{a}+\mathrm{b} i .)\end{array} \)
Ask by Griffin Hodges. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(-2i\)
Solution
Calculate or simplify the expression \( -\sqrt{-4} \).
Calculate the value by following steps:
- step0: Calculate:
\(-\sqrt{-4}\)
- step1: Simplify the root:
\(-2i\)
The expression \(-\sqrt{-4}\) can be simplified to \(-2i\).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
To simplify \(-\sqrt{-4}\), we start by recognizing that \(-4\) can be rewritten as \(4 \cdot (-1)\). Therefore, we have: \[ -\sqrt{-4} = -\sqrt{4 \cdot (-1)} = -\sqrt{4} \cdot \sqrt{-1} \] This simplifies to: \[ -\sqrt{4} \cdot i = -2i \] So the expression becomes: \(-\sqrt{-4} = 0 - 2i\) In the form \(a + bi\), this means: \[-\sqrt{-4} = 0 - 2i\]
