Найти комплексное число z такое, что a) z (1 + i) = 1 б) z (2 + i) = 1-i в) z (2 + 3i) = 3-2i г) z (1 + i) = 3 + 4i

a) z ⋅ (1 + i) = 1,

z = 1 / (1 + i) = 1 ⋅ (1 - i) / [ (1 + i) ⋅ (1 - i) ] = (1 - i) / (1² - i²) = (1 - i) / (1 + 1) = 0,5 - 0,5i.

б) z ⋅ (2 + i) = 1 - i,

z = (1 - i) / (2 + i) = (1 - i) ⋅ (2 - i) / [ (2 + i) ⋅ (2 - i) ] = (2 - 2i - i - i²) / (4 - i²) = (3 - 3i) / 5 =

= 0,6 - 0,6i.

в) z ⋅ (2 + 3i) = 3 - 2i,

z = (3 - 2i) / (2 + 3i) = (3 - 2i) ⋅ (2 - 3i) / [ (2 + 3i) ⋅ (2 - 3i) ] =

= (6 - 4i - 9i + 6i²) / (4 - 9i²) = - 13i / 13 = - i.

г) z ⋅ (1 + i) = 3 + 4i,

z = (3 + 4i) / (1 + i) = (3 + 4i) ⋅ (1 - i) / [ (1 + i) ⋅ (1 - i) ] =

= (3 + 4i - 3i - 4i²) / (1 - i²) = (7 + i) / 2 = 3,5 + 0,5i.