Câu hỏi:
Số phức \(z = \dfrac{{3 + 4i}}{{2 + 3i}} + \dfrac{{5 – 2i}}{{2 – 3i}}\) bằng:
-
A.
\(\dfrac{{34}}{{13}} + \dfrac{{10}}{{13}}i\). -
B.
\(\dfrac{{34}}{{13}} – \dfrac{{10}}{{13}}i\). -
C.
\( – \dfrac{{34}}{{13}} + \dfrac{{10}}{{13}}i\). -
D.
\( – \dfrac{{34}}{{13}} – \dfrac{{10}}{{13}}i\).
Lời giải tham khảo:
Đáp án đúng: A
\(\begin{array}{l}z = \dfrac{{3 + 4i}}{{2 + 3i}} + \dfrac{{5 – 2i}}{{2 – 3i}}\\\,\,\,\, = \dfrac{{\left( {3 + 4i} \right)\left( {2 – 3i} \right) + \left( {5 – 2i} \right)\left( {2 + 3i} \right)}}{{4 – 9{i^2}}}\\\,\,\,\, = \dfrac{{6 – i – 12{i^2} + 10 + 11i – 6{i^2}}}{{13}}\\\,\,\,\, = \dfrac{{34}}{{13}} + \dfrac{{10}}{{13}}i\end{array}\)
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