Let z be a complex number satisfying 2z + 3*(Conjugate Z) = -25 - 8i. What is the value of z?
z = a + bi z conjugate = a - bi
So
2 ( a + bi) + 3 ( a - bi) = -25 - 8i
2a + 2bi +3a - 3bi = -25 - 8i
(2a + 3a) = - 25 and ( 2b - 3b)i = -8i
5a = -25 -bi = -8i
a = -5 b = 8
z = -5 + 8i
