Question
Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \( -8+\sqrt{-81} \) \begin{tabular}{|l}\hline\( i \) \\ \hline\end{tabular}
Ask by Patel Barker. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
-8 + 9i
\]
Solution
To rewrite the expression \( -8 + \sqrt{-81} \) as a complex number using the imaginary unit \( i \), follow these steps:
1. **Simplify the Radical:**
\[
\sqrt{-81} = \sqrt{81 \times (-1)} = \sqrt{81} \times \sqrt{-1} = 9i
\]
2. **Substitute Back into the Expression:**
\[
-8 + \sqrt{-81} = -8 + 9i
\]
**Final Answer:**
\[
-8 + 9i
\]
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Beyond the Answer
To rewrite the expression \( -8+\sqrt{-81} \) as a complex number, we start by recognizing that \( \sqrt{-81} \) can be expressed using the imaginary unit \( i \). Specifically, we have: \[ \sqrt{-81} = \sqrt{81} \cdot \sqrt{-1} = 9i \] Now, substituting this back into the original expression gives us: \[ -8 + \sqrt{-81} = -8 + 9i \] Thus, the expression simplifies to: \[ -8 + 9i \] And there you have it! The complex number form of the expression is \( -8 + 9i \).
