1. **State the problem:** Solve for $x$ and $y$ in the equation $(x+yi)(-i)=3$ where $x$ and $y$ are real numbers. 2. **Recall the formula and rules:** Multiplying complex numbers follows distributive property and $i^2 = -1$. 3. **Expand the left side:** $$ (x+yi)(-i) = x(-i) + yi(-i) = -xi - y i^2 $$ 4. **Simplify using $i^2 = -1$:** $$ -xi - y(-1) = -xi + y $$ 5. **Rewrite the expression:** $$ y - xi $$ 6. **Express in standard form $a + bi$:** $$ y + (-x)i $$ 7. **Set equal to the right side:** $$ y + (-x)i = 3 + 0i $$ 8. **Equate real and imaginary parts:** - Real part: $y = 3$ - Imaginary part: $-x = 0 \Rightarrow x = 0$ 9. **Final answer:** $$ x = 0, \quad y = 3 $$