Pregunta
Write in terms of \( i \). Simplify your answer as much as possible. \[ -\sqrt{-11} \]
Ask by Guzman O'Quinn. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\(-i\sqrt{11}\)
Solución
To express \(-\sqrt{-11}\) in terms of \(i\), follow these steps:
1. **Rewrite the square root of a negative number using \(i\):**
\[
\sqrt{-11} = \sqrt{11} \cdot \sqrt{-1} = \sqrt{11} \cdot i = i\sqrt{11}
\]
2. **Apply the negative sign:**
\[
-\sqrt{-11} = -i\sqrt{11}
\]
So, the simplified expression in terms of \(i\) is:
\[
- i \sqrt{11}
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Beyond the Answer
To simplify \(-\sqrt{-11}\) in terms of \(i\), we start by recognizing that \(i\) is defined as \(i = \sqrt{-1}\). We can rewrite the expression as follows: \[ -\sqrt{-11} = -\sqrt{11} \sqrt{-1} = -\sqrt{11} \cdot i \] Thus, the simplified form of \(-\sqrt{-11}\) is: \[ -\sqrt{11} i \]
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