КОМПЛЕКСНЫЕ ЧИСЛА, вариант 2, 4-5 задания

(2 + i√12)² = 2² + 2*2*i√12 + (i√12)² = 4 + 8i√3 - 12 = -8 + i8√3

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z² - (4 + 3i)z + 1 + 5i = 0

D = (4 + 3i)² - 4(1 + 5i) = 16 + 2*4*3i + (3i)² - 4 - 20i = 16 + 24i - 9 - 4 - 20i = 3 + 4i = 4 + 4i - 1 = 2² + 2*2*i + i² = (2 + i)²

√D = 2 + i

z1 = ( (4 + 3i) + (2 + i))/2  = (6 + 4i)/2 = 3 + 2i

z2 = ( (4 + 3i) - (2 + i))/2 = (2 + 2i)/2 = 1 + i