Упр.13.28 ГДЗ Мерзляк 11 класс Углубленный уровень (Алгебра)

1) 3/(-i); 2) 5i/(3+2i); 3) (7+i)/(2+i); 4) (4-5i)/(4+5i).

1. $$\frac{3}{-i}=\frac{3i}{-i^2}=\frac{3i}{-(-1)}=3i.$$

2. $$\frac{5i}{3+2i}=\frac{5i(3-2i)}{(3+2i)(3-2i)}=\frac{15i-10i^2}{9-4i^2}=\frac{10+15i}{13}=\frac{10}{13}+\frac{15}{13}i.$$

3. $$\frac{7+i}{2+i}=\frac{(7+i)(2-i)}{(2+i)(2-i)}=\frac{14-7i+2i-i^2}{4-i^2}=\frac{15-5i}{5}=3-i.$$

4. $$\frac{4-5i}{4+5i}=\frac{(4-5i)^2}{(4+5i)(4-5i)}=\frac{16-40i+25i^2}{16-25i^2}=\frac{-9-40i}{41}=-\frac{9}{41}-\frac{40}{41}i.$$

Ответ

1) $$3i$$; 2) $$\frac{10}{13}+\frac{15}{13}i$$; 3) $$3-i$$; 4) $$-\frac{9}{41}-\frac{40}{41}i$$.