Question

Срочно нужна помощь!

Answer 1

1.а)2-3і+2і+3=5-і
б) 2-3і+3-2і=5-5і
в)2-3і-2і-3=-1-5і
г)2і+3-3+2і=4і
д)(2-3і)(2і+3)=4і+6+6-9і=12-5і
е)(3-2і)(2і+3)=(3-2і)(3+2і)=3²-(2і)²=9+4=13

2.
(2-і)(2+і)-(3-2і)+7=2²-і²-3+2і+7=4+1-3+2і+7=9+2і

3.а)
$\frac{1}{i} = \frac{1 \times \: i }{i \times i} = \frac{i}{ - 1} = - i$
б)
$\frac{1}{2 + i} = \frac{1 \times (2 - i)}{(2 + i)(2 - i)} = \\ = \frac{2 - i}{ {2}^{2} - i^{2} } = \frac{2 - i }{4 + 1} = \\ = \frac{2 - i}{5} = \frac{2}{5} - \frac{1}{5} i = \\ = 0.4 - 0.2i$
в)
$\frac{3 -i }{2 + 2i} = \frac{(3 - i)(2 - 2i)}{(2 + 2i)(2 - 2i)} = \\ = \frac{6 - 6i - 2i - 2}{ {2}^{2} - {(2i)}^{2} } = \\ = \frac{4 - 8i}{4 + 4} = \frac{4 - 8i}{8} = \\ = \frac{4}{8} - \frac{8}{8} i = 0.5 - i$