1. We start with the given equation: $$\frac{(4 - i)(4 + i)}{2 - i} = x + yi$$ 2. Simplify the numerator by using the difference of squares formula: $$(4 - i)(4 + i) = 4^2 - i^2 = 16 - (-1) = 16 + 1 = 17$$ So the expression becomes: $$\frac{17}{2 - i} = x + yi$$ 3. To simplify the division by a complex number, multiply numerator and denominator by the complex conjugate of the denominator: $$\frac{17}{2 - i} \times \frac{2 + i}{2 + i} = \frac{17(2 + i)}{(2 - i)(2 + i)}$$ 4. Simplify the denominator: $$(2 - i)(2 + i) = 2^2 - i^2 = 4 - (-1) = 4 + 1 = 5$$ 5. Therefore: $$\frac{17(2 + i)}{5} = \frac{34 + 17i}{5} = \frac{34}{5} + \frac{17}{5}i$$ 6. Equate real and imaginary parts to $x$ and $y$ respectively: $$x = \frac{34}{5} = 6.8$$ $$y = \frac{17}{5} = 3.4$$ 7. Final answer: $$x = 6.8, y = 3.4$$