Hãy thu gọn số phức (z = dfrac{{3 + 2i}}{{1 – i}} + dfrac{{1 – i}}{{3 + 2i}}), ta được:

(eqalign{z& = dfrac{{3 + 2i}}{{1 – i}} + dfrac{{1 – i}}{{3 + 2i}}cr& = dfrac{{{{left( {3 + 2i} right)}^2} + {{left( {1 – i} right)}^2}}}{{left( {1 – i} right)left( {3 + 2i} right)}}cr&= dfrac{{9 + 4{i^2} + 12i + 1 + {i^2} – 2i}}{{3 – 2{i^2} – i}}cr& = dfrac{{5 + 10i}}{{5 – i}}cr& = dfrac{{5(1 + 2i)(5 + i)}}{{25 – {i^2}}}cr& = dfrac{{5(5 + 2{i^2} + 11i)}}{{26}}cr&= dfrac{{5(3 + 11i)}}{{26}} = dfrac{{15}}{{26}} + dfrac{{55}}{{26}}icr})