(1+i)(2−i)=()(1+i)(2-i)=()
A. −3−i-3-i
B. −3+i-3+i
C. 3−i3-i
D. 3+i3+i

Four operationsConcept of complex numbers
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Worked solution

1. 展开复数乘法算式

(1+i)(2−i)=1×2−1×i+2×i−i2(1+i)(2-i) = 1 \times 2 - 1 \times i + 2 \times i - i^2

2. 代入 $i^2 = -1$ 并合并同类项得到最终结果

由于 i2=−1i^2 = -1，代入上式可得：
2+i−(−1)=3+i2 + i - (-1) = 3 + i
对照选项，应选 D。

Answer

D

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