1. **Stating the problem:** Find the conjugate of the polynomial expression $3 + 4i$. 2. **Formula and explanation:** The conjugate of a complex number $a + bi$ is $a - bi$. This means we change the sign of the imaginary part. 3. **Apply the formula:** For $3 + 4i$, the conjugate is $3 - 4i$. 4. **Intermediate work:** $$\text{Conjugate} = 3 + 4i \to 3 - 4i$$ 5. **Explanation:** The conjugate flips the sign of the imaginary part, which is useful in simplifying expressions and dividing complex numbers. **Final answer:** The conjugate of $3 + 4i$ is $3 - 4i$.