Question

Даны комплексные числа z_1 и z_2. Вычислить w=(z_1∙z_2)/z_3 , где z_3=z_1+z_2. Для контроля проверить равенство wz_3=z_1 z_2. 3. z_1=1+i, z_2=2-2i.

Answer 1

$z_1 = 1+i =(z_{11};z_{12})\ z_2 = 2-2i =(z_{21};z_{22})\ z_{11} = 1;z_{12}=1;z_{21} = 2;z_{22}=-2;\ \ z_1*z_2 = (z_{11}z_{21} - z_{12}z_{22}) + i(z_{11}z_{22}+z_{12}z_{21})=4\ z_3 = z_1 + z_2 = (z_{11}+z_{21}) + i (z_{12}+z_{22}) = 3 - i\ \ w = frac{4}{3-i} = frac{12}{10}+frac{4}{10}i = frac{4}{10}(3+i)\ \ w*z_3 = frac{4}{10}(3+i)(3-i) = frac{4}{10}(3*3+1*1) = 4$