1. **State the problem:** Simplify the expression $$(3 - )(9 - 2i)(1 + 3i)$$. Since the first term is incomplete, assuming it is $3$ (without any imaginary part), the expression becomes $$3 \times (9 - 2i) \times (1 + 3i)$$.
2. **Recall the formula:** To multiply complex numbers, use the distributive property and remember that $$i^2 = -1$$.
3. **First multiply** $$(9 - 2i)(1 + 3i)$$:
$$\begin{aligned}
(9 - 2i)(1 + 3i) &= 9 \times 1 + 9 \times 3i - 2i \times 1 - 2i \times 3i \\
&= 9 + 27i - 2i - 6i^2 \\
&= 9 + 25i - 6(-1) \\
&= 9 + 25i + 6 \\
&= 15 + 25i
\end{aligned}$$
4. **Now multiply** $$3 \times (15 + 25i)$$:
$$3 \times 15 + 3 \times 25i = 45 + 75i$$
5. **Final answer:** $$\boxed{45 + 75i}$$
Complex Multiplication E7E2Ec
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