Question

Выражение, , надо 1) (1-2i)(2+i)/3-2i 2) 2+3i/(4+i)(2-2i) 3) 1/i

Answer 1

$1)\quad \frac{(1-2i)(2+i)}{3-2i}= \frac{2-3i-2i^2}{3-2i} = \frac{(4-3i)(3+2i)}{(3-2i)(3+2i)} = \frac{12-i-6i^2}{9-4i^2} =\\\\= \frac{18-i}{9+4} = \frac{18}{13} -\frac{1}{13}i\\\\2)\quad \frac{2+3i}{(4+i)(2-2i)}= \frac{2+3i}{8-6i-2i^2}=\frac{2+3i}{10-6i} = \frac{(2+3i)(10+6i)}{(10-6i)(10+6i)} =\\\\=\frac{20+42i+18i^2}{100-36i^2} = \frac{2+42i}{136}=\frac{1}{68}+\frac{21}{68}i\\\\3)\quad \frac{1}{i} =\frac{i}{i^2} =\frac{i}{-1} =-i$