Question

Комплексные числа Решите уравнение: а)z^2+z+2=0 б) z^2-(3-2i)z+5-5i=0

Answer 1

Z^2 + z + 2 = 0 
D = 1 - 8 = - 7
z1 = ( - 1 + i √7)/2 
z2 = ( - 1 - i √7)/2

z^2 - (3 - 2i)z + 5 - 5i = 0
D = (3 - 2i)^2 - 4*(5 - 5i) = 8i - 15
z1 = (3 - 2i + √(8i - 15))/2 = (3 - 2i + 1 + 4i)/2 = 2 + i
z2 = (3 - 2i - √(8i - 15))/2 = (3 - 2i - 1 - 4i)/2 = 1 - 3i

√(8i - 15) = ± (1 + 4i)
a = ± 1
b = ± 4