posted by Anne .
the complex number Z satisfies
please help thx!
Multipy both sides of the equation by Z+4, and combine terms.
Z = (3 + 2i)(Z+4) = 3Z + 2iZ +12 + 8i
(2 + 2i)Z + 12 + 8i = 0
Z = -(12 + 8i)/(2 + 2i)
= -(6 + 4i)/(i + 1)
= -(6 + 4i)(i -1)/[(i+1)(i -1)]
= -(-6 +2i -4)/(-2)
Z = -5 + i
i don't really get how 3Z + 2iZ +12 + 8i can be transformed into (2 + 2i)Z + 12 + 8i = 0
why is it not (3 + 2i)Z + 12 + 8i = 0??
Compare the first two equations.
I subtracted Z from both sides of the first equation, to get a zero on one side of the equation.