1. **State the problem:** Find real numbers $a$ and $b$ such that $a + bi = -9 + 4i$. 2. **Recall the rule:** Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal. 3. **Set up equations:** - Real parts: $a = -9$ - Imaginary parts: $b = 4$ 4. **Solution:** - $a = -9$ - $b = 4$ Thus, the values of $a$ and $b$ that satisfy the equation are $a = -9$ and $b = 4$.