Bài 5 trang 136 SGK Giải tích 12

Tính:

a) \((2 + 3i)^2\);                       b) \((2 + 3i)^3\)

\(\begin{array}{l}a)\,\,{\left( {2 + 3i} \right)^2}\\\,\,\, = {2^2} + 2.2.3i + {\left( {3i} \right)^2}\\\,\,\, = 4 + 12i - 9\\\,\,\, = - 5 + 12i\\b)\,\,{\left( {2 + 3i} \right)^3}\\\,\,\, = {2^3} + {3.2^2}.3i + 3.2.{\left( {3i} \right)^2} + {\left( {3i} \right)^3}\\\,\,\, = 8 + 36i - 54 - 27i\\\,\,\, = - 46 + 9i\end{array}\)