Дано: z₁= 5 + i, z₂ = 8 - i.
Найти 1) z₁+z₂; 2)z₁ - z₂; 3) z₁·z₂; 4)z₁/z₂
Решение
1) z₁+z₂ = 5 + i + 8 - i = 5 + 8 + i - i = 13
2) z₁ - z₂ = 5 + i - (8 - i) = 5 - 8 + i + i = -3 + 2i
3) z₁·z₂ =(5 + i)·(8 - i) = 5·8 - 5i + 8i - i² = 40 + 3i - (-1) = 41 + 3i
![\frac{z_1}{z_2}= \frac{5+i}{8-i}= \frac{(5+i)(8+i)}{(8-i)(8+i)}= \frac{40+5i+8i+i^2}{8^2-i^2}= \frac{39+13i}{64-(-1)}= \frac{39+13i}{65}= \frac{z_1}{z_2}= \frac{5+i}{8-i}= \frac{(5+i)(8+i)}{(8-i)(8+i)}= \frac{40+5i+8i+i^2}{8^2-i^2}= \frac{39+13i}{64-(-1)}= \frac{39+13i}{65}=](https://tex.z-dn.net/?f=%5Cfrac%7Bz_1%7D%7Bz_2%7D%3D+%5Cfrac%7B5%2Bi%7D%7B8-i%7D%3D+%5Cfrac%7B%285%2Bi%29%288%2Bi%29%7D%7B%288-i%29%288%2Bi%29%7D%3D+%5Cfrac%7B40%2B5i%2B8i%2Bi%5E2%7D%7B8%5E2-i%5E2%7D%3D+%5Cfrac%7B39%2B13i%7D%7B64-%28-1%29%7D%3D+%5Cfrac%7B39%2B13i%7D%7B65%7D%3D++)