Write in terms of \( i \). Simplify your answer as much as possible \( \quad-\sqrt{-4} \)

To simplify the expression \( -\sqrt{-4} \) in terms of the imaginary unit \( i \), follow these steps: 1. **Understand the Imaginary Unit \( i \):** The imaginary unit \( i \) is defined as: \[ i = \sqrt{-1} \] 2. **Simplify \( \sqrt{-4} \):** Break down the expression inside the square root: \[ \sqrt{-4} = \sqrt{4 \times (-1)} = \sqrt{4} \times \sqrt{-1} \] Compute each part: \[ \sqrt{4} = 2 \quad \text{and} \quad \sqrt{-1} = i \] Therefore: \[ \sqrt{-4} = 2i \] 3. **Apply the Negative Sign:** Now, apply the negative sign to the simplified square root: \[ -\sqrt{-4} = -2i \] **Final Answer:** \[ -2i \]