1. **State the problem:** Identify which numbers from the list are complex numbers. 2. **Recall the definition:** A complex number is any number that can be written in the form $a + bi$ where $a$ and $b$ are real numbers and $i = \sqrt{-1}$. 3. **Analyze each number:** - $5 - \sqrt{\frac{9}{4}} = 5 - \frac{3}{2} = 3.5$ which is a real number, not complex. - $1 + \sqrt{-3} = 1 + \sqrt{3}i$ since $\sqrt{-3} = \sqrt{3}i$, this is complex. - $4 + 3\sqrt{-16} = 4 + 3 \times 4i = 4 + 12i$ which is complex. - $\frac{4 - \sqrt{12}}{-3} = \frac{4 - 2\sqrt{3}}{-3}$ is real because $\sqrt{12}$ is real, so this is real. - $\frac{3 + 2\sqrt{-9}}{7} = \frac{3 + 2 \times 3i}{7} = \frac{3 + 6i}{7} = \frac{3}{7} + \frac{6}{7}i$ which is complex. 4. **Final answer:** The complex numbers are: - $1 + \sqrt{-3}$ - $4 + 3\sqrt{-16}$ - $\frac{3 + 2\sqrt{-9}}{7}$ **Summary:** $$\text{Complex numbers} = \left\{1 + \sqrt{-3},\ 4 + 3\sqrt{-16},\ \frac{3 + 2\sqrt{-9}}{7}\right\}$$