Упр.732 ГДЗ Колягин Ткачёва 11 класс (Алгебра)

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

1. $$ (2-i)^3=2^3-3\cdot 2^2 i+3\cdot 2 i^2-i^3 $$
   $$ =8-12i-6+i=2-11i. $$
2. $$ \left(\frac{1+i}{1-i}\right)^4=\left(\frac{(1+i)^2}{(1-i)(1+i)}\right)^4 $$
   $$ =\left(\frac{1+2i+i^2}{1-i^2}\right)^4=\left(\frac{1+2i-1}{1+1}\right)^4 $$
   $$ =\left(\frac{2i}{2}\right)^4=i^4=1. $$
3. $$ (2+3i)^2-(2-3i)^2 $$
   $$ =(4+12i+9i^2)-(4-12i+9i^2)=24i. $$
4. $$ (3+4i)^2+(3-4i)^2 $$
   $$ =(9+24i+16i^2)+(9-24i+16i^2)=18+32i^2 $$
   $$ =18-32=-14. $$

Ответ

1) $$2-11i$$; 2) $$1$$; 3) $$24i$$; 4) $$-14$$.