Câu hỏi:
Tìm số phức \(\bar z\) thỏa mãn \(\frac{{2 + i}}{{1 – i}}z = \frac{{ – 1 + 3i}}{{2 + i}}\)
- A. \(\frac{{22}}{{25}} + \frac{4}{{25}}i\)
- B. \(\frac{{22}}{{25}} – \frac{4}{{25}}i\)
- C. \(\frac{{22}}{{25}}i + \frac{4}{{25}}\)
- D. \( – \frac{{22}}{{25}} + \frac{4}{{25}}i\)
Đáp án đúng: B
Ta có:
\(\frac{{2 + i}}{{1 – i}}z = \frac{{ – 1 + 3i}}{{2 + i}} \Rightarrow z = \frac{{\left( { – 1 + 3i} \right)\left( {1 – i} \right)}}{{{{\left( {2 + i} \right)}^2}}}\)
\( = \frac{{\left( { – 1 + 3i} \right)\left( {1 – i} \right){{\left( {2 – i} \right)}^2}}}{{25}} = \frac{{22}}{{25}} + \frac{4}{{25}}i\)
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