Câu hỏi:
Cho số phức \(z = \frac{{{{\left( {1 + i} \right)}^{100}}}}{{{{\left( {1 + i} \right)}^{96}} – i{{\left( {1 + i} \right)}^{98}}}}\). Khi đó:
- A. \(\left| z \right| = \frac{4}{3}\)
- B. \(\left| z \right| = \frac{1}{2}\)
- C. \(\left| z \right| = \frac{3}{4}\)
- D. \(\left| z \right| = 1\)
Đáp án đúng: A
Ta có: \(z = \frac{{{{\left( {1 + i} \right)}^{96}}.{{\left( {1 + i} \right)}^4}}}{{{{\left( {1 + i} \right)}^{96}}\left[ {1 – i{{\left( {1 + i} \right)}^2}} \right]}} = \frac{{{{\left( {1 + i} \right)}^4}}}{{1 – i{{\left( {1 + i} \right)}^2}}} = \frac{{{{\left( {1 + 2i + {i^2}} \right)}^2}}}{{1 – i\left( {1 + 2i + {i^2}} \right)}}\)
\( = \frac{{4{i^2}}}{{1 – 2{i^2}}} = – \frac{4}{3} \Rightarrow \left| z \right| = \frac{4}{3}\)
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