Bài 8. Thực hiện các phép tính sau:
a) (3 + 2i)[(2 – i) + (3 – 2i)]
b) (4 - 3i) + {{1 + i} \over {2 + i}}
c) (1 + i)^2 – (1 – i)^2
d) {{3 + i} \over {2 + i}} - {{4 - 3i} \over {2 - i}}
a) (3 + 2i)[(2 – i) + (3 – 2i)]= (3 + 2i)(5 – 3i) = 21 + i
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b)
\eqalign{ & (4 - 3i) + {{1 + i} \over {2 + i}} = (4 - 3i) + {{(1 + i)(2 - i)} \over 5} = (4 - 3i)({3 \over 5} + {1 \over 5}i) \cr & = (4 + {3 \over 5}) - (3 - {1 \over 5})i = {{23} \over 5} - {{14} \over 5}i \cr}
c) (1 + i)^2 – (1 – i)^2 = 2i – (-2i) = 4i
d)
\eqalign{ & {{3 + i} \over {2 + i}} - {{4 - 3i} \over {2 - i}} = {{(3 + i)(2 - i)} \over 5} - {{(4 - 3i)(2 + i)} \over 5} \cr & = {{7 - i} \over 5} - {{11 - 2i} \over 5} = {{ - 4} \over 5} + {1 \over 5}i \cr}