Упр.16.19 ГДЗ Никольский Потапов 11 класс (Алгебра)

б) (3-2i)2;
в) (4+i)2;
г) (3-3i)2;
д) (4+4i)2;
е) (5-5i)2;
ж) (1+i)2;
з) (1-2i)2;
и) (2+i)2.

1. $$\begin{aligned} (5+2i)^2&=25+20i+4i^2\\ &=25-4+20i\\ &=21+20i \end{aligned}$$
2. $$\begin{aligned} (3-2i)^2&=9-12i+4i^2\\ &=9-4-12i\\ &=5-12i \end{aligned}$$
3. $$\begin{aligned} (4+i)^2&=16+8i+i^2\\ &=16-1+8i\\ &=15+8i \end{aligned}$$
4. $$\begin{aligned} (3-3i)^2&=9-18i+9i^2\\ &=9-18i-9\\ &=-18i \end{aligned}$$
5. $$\begin{aligned} (4+4i)^2&=16+32i+16i^2\\ &=16-16+32i\\ &=32i \end{aligned}$$
6. $$\begin{aligned} (5-5i)^2&=25-50i+25i^2\\ &=25-25-50i\\ &=-50i \end{aligned}$$
7. $$\begin{aligned} (1+i)^3&=(1+i)^2(1+i)\\ &=(1+2i+i^2)(1+i)\\ &=(2i)(1+i)\\ &=2i+2i^2\\ &=-2+2i \end{aligned}$$
8. $$\begin{aligned} (1-2i)^3&=(1-2i)^2(1-2i)\\ &=(1-4i+4i^2)(1-2i)\\ &=(-3-4i)(1-2i)\\ &=-3+6i-4i+8i^2\\ &=-11+2i \end{aligned}$$
9. $$\begin{aligned} (2+i)^3&=(2+i)^2(2+i)\\ &=(4+4i+i^2)(2+i)\\ &=(3+4i)(2+i)\\ &=6+3i+8i+4i^2\\ &=2+11i \end{aligned}$$

Ответ

а) $$21+20i$$; б) $$5-12i$$; в) $$15+8i$$; г) $$-18i$$; д) $$32i$$; е) $$-50i$$; ж) $$-2+2i$$; з) $$-11+2i$$; и) $$2+11i$$.