Question
Express \( -9 \sqrt{-16} \) as a complex number (in terms of \( i \) ): \( -9 \sqrt{-16}=\square \)
Ask by Mills Morrison. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(-36i\)
Solution
To express \( -9 \sqrt{-16} \) as a complex number in terms of \( i \), follow these steps:
1. **Simplify the square root:**
\[
\sqrt{-16} = \sqrt{16 \times (-1)} = \sqrt{16} \times \sqrt{-1} = 4i
\]
2. **Multiply by \(-9\):**
\[
-9 \times 4i = -36i
\]
So, the expression \( -9 \sqrt{-16} \) as a complex number is:
\[
-9 \sqrt{-16} = -36i
\]
**Answer:**
\(-36i\)
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Simplify this solution Extra Insights
To express \( -9 \sqrt{-16} \) as a complex number, we first simplify \( \sqrt{-16} \). We know that \( \sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i \). Now, substituting this back into the original expression, we have: \[ -9 \sqrt{-16} = -9 \cdot 4i = -36i. \] Thus, \( -9 \sqrt{-16} = -36i \).
