Advertisements (Quảng cáo)
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) \((3 + 2i)[(2 – i) + (3 – 2i)]= (3 + 2i)(5 – 3i) = 21 + i\)
b)
Advertisements (Quảng cáo)
\(\eqalign{
& (4 – 3i) + {{1 + i} \over {2 + i}} = (4 – 3i) + {{(1 + i)(2 – i)} \over 5} = (4 – 3i)({3 \over 5} + {1 \over 5}i) \cr
& = (4 + {3 \over 5}) – (3 – {1 \over 5})i = {{23} \over 5} – {{14} \over 5}i \cr} \)
c) \((1 + i)^2 – (1 – i)^2 = 2i – (-2i) = 4i\)
d)
\(\eqalign{
& {{3 + i} \over {2 + i}} – {{4 – 3i} \over {2 – i}} = {{(3 + i)(2 – i)} \over 5} – {{(4 – 3i)(2 + i)} \over 5} \cr
& = {{7 – i} \over 5} – {{11 – 2i} \over 5} = {{ – 4} \over 5} + {1 \over 5}i \cr} \)