Use the imaginary number \( i \) to rewrite the expression below as a complex number. Simplify all radicals. \[ -3+\sqrt{-4} \]

To rewrite the expression \(-3 + \sqrt{-4}\) as a complex number using the imaginary unit \( i \), follow these steps: 1. **Express \(\sqrt{-4}\) in terms of \( i \):** The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \). Therefore, we can rewrite \(\sqrt{-4}\) as: \[ \sqrt{-4} = \sqrt{4 \times (-1)} = \sqrt{4} \times \sqrt{-1} = 2i \] 2. **Substitute back into the original expression:** \[ -3 + \sqrt{-4} = -3 + 2i \] 3. **Final Complex Number:** The expression simplified as a complex number is: \[ -3 + 2i \] This is in the standard form \( a + bi \), where: - \( a = -3 \) (the real part) - \( b = 2 \) (the imaginary part) **Answer:** \(-3 + 2i\)