Express $$ \sqrt{-64} $$ as a complex number, in terms of $$ i $$ : $$ \sqrt{-64}=\square $$

Question

UpStudy AI · Accepted Answer

To express $$ \sqrt{-64} $$ as a complex number in terms of $$ i $$, follow these steps:

1. **Recognize the imaginary unit**:
   $$
   i = \sqrt{-1}
   $$

2. **Factor the expression**:
   $$
   \sqrt{-64} = \sqrt{64 \times (-1)} = \sqrt{64} \times \sqrt{-1}
   $$

3. **Simplify the square roots**:
   $$
   \sqrt{64} = 8 \quad \text{and} \quad \sqrt{-1} = i
   $$

4. **Combine the results**:
   $$
   \sqrt{-64} = 8i
   $$

**Final Answer:**
$$
\sqrt{-64} = 8i
$$
$$ \sqrt{-64} = 8i $$

Express \( \sqrt{-64} \) as a complex number, in terms of \( i \) : \( \sqrt{-64}=\square \)