1. **Problem Statement:** Find the conjugate of the complex number $z = a + bi$, where $a$ and $b$ are real numbers and $i$ is the imaginary unit. 2. **Formula:** The conjugate of a complex number $z = a + bi$ is given by $\overline{z} = a - bi$. 3. **Explanation:** The conjugate changes the sign of the imaginary part while keeping the real part the same. 4. **Example:** If $z = 3 + 4i$, then its conjugate is $$\overline{z} = 3 - 4i$$ 5. **Intermediate step:** Writing the conjugate explicitly, $$\overline{z} = a + \cancel{bi} - 2\cancel{bi} = a - bi$$ 6. **Final answer:** The conjugate of $z = a + bi$ is $$\boxed{a - bi}$$