Câu 1:Trang 138-sgk giải tích 12
Thực hiện các phép chia sau:
a) $\frac{2+i}{3-2i}$
b) $\frac{1+i\sqrt{2}}{2+i\sqrt{3}}$
c) $\frac{5i}{2-3i}$
d) $\frac{5-2i}{i}$
Bài Làm:
a) $\frac{2+i}{3-2i}$
= $\frac{(2+i)(3+2i)}{(3-2i)(3+2i)}$
= $\frac{4+7i}{13}$
= $\frac{4}{13}+\frac{7i}{13}$
b) $\frac{1+i\sqrt{2}}{2+i\sqrt{3}}$
= $\frac{(1+i\sqrt{2})(2-i\sqrt{3})}{(2+i\sqrt{3})(2-i\sqrt{3})}$
= $\frac{2+\sqrt{6}}{7}+\frac{2\sqrt{2}-\sqrt{3}i}{7}$
c) $\frac{5i}{2-3i}$
= $\frac{5i(2+3i)}{(2-3i)(2+3i)}$
= $\frac{15+10i}{13}$
= $\frac{15}{13}+\frac{10i}{13}$
d) $\frac{5-2i}{i}$
= $(5-2i)(-i)$
= $-2-5i$