which of the following numbers is an imaginary number ?

Options

A. `sqrt(64)`
B. `sqrt(11)`
C. `-4/(sqrr(3))`
D. `-sqrt(-64)`

Answer

To determine which of the following numbers is an imaginary number, we need to analyze each option provided:

1. **Option A: \( \sqrt{64} \)**
- Calculation: \( \sqrt{64} = 8 \)
- Conclusion: This is a real number, not an imaginary number.

2. **Option B: \( \sqrt{11} \)**
- Calculation: \( \sqrt{11} \) is approximately \( 3.3166 \)
- Conclusion: This is also a real number, not an imaginary number.

3. **Option C: \( -\frac{4}{\sqrt{3}} \)**
- Calculation: This simplifies to a negative real number, approximately \( -2.3094 \)
- Conclusion: This is a real number, not an imaginary number.

4. **Option D: \( -\sqrt{-64} \)**
- Calculation:
- First, we recognize that \( \sqrt{-64} = \sqrt{64} \cdot \sqrt{-1} = 8i \) (where \( i \) is the imaginary unit).
- Therefore, \( -\sqrt{-64} = -8i \).
- Conclusion: This is an imaginary number.

Based on the analysis, the correct answer is **Option D: \( -\sqrt{-64} \)**, which is an imaginary number.