Question
Express \( 4+\sqrt{-81} \) as a complex number \( 4+\sqrt{-81}=\square \)
Ask by Weston Gough. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 4 + \sqrt{-81} = 4 + 9i \)
Solution
To express \( 4 + \sqrt{-81} \) as a complex number, follow these steps:
1. **Understand the Square Root of a Negative Number:**
\[
\sqrt{-81} = \sqrt{81 \times (-1)} = \sqrt{81} \times \sqrt{-1} = 9i
\]
Here, \( i \) is the imaginary unit, defined by \( i^2 = -1 \).
2. **Combine the Real and Imaginary Parts:**
\[
4 + \sqrt{-81} = 4 + 9i
\]
So, the complex number representation is:
\[
4 + \sqrt{-81} = 4 + 9i
\]
**Answer:**
\( 4 + \sqrt{-81} = 4 + 9i \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To express \( 4+\sqrt{-81} \) as a complex number, we first need to simplify \( \sqrt{-81} \). The square root of a negative number can be expressed using the imaginary unit \( i \), where \( i = \sqrt{-1} \). Therefore, we have: \[ \sqrt{-81} = \sqrt{81} \cdot \sqrt{-1} = 9i \] Now substituting this back into the expression, we get: \[ 4 + \sqrt{-81} = 4 + 9i \] So, \( 4+\sqrt{-81} = 4 + 9i \).
