1. The problem is to simplify the complex fraction $$\frac{2 + 7i}{4 - 2i}$$. 2. To simplify a complex fraction, multiply the numerator and denominator by the conjugate of the denominator. 3. The conjugate of $$4 - 2i$$ is $$4 + 2i$$. 4. Multiply numerator and denominator by $$4 + 2i$$: $$\frac{2 + 7i}{4 - 2i} \times \frac{4 + 2i}{4 + 2i}$$ 5. This step removes the imaginary part from the denominator, making it a real number. Answer: You multiply the numerator and denominator by $$4 + 2i$$.