Calculuscomplex numbers
posted by Anne on .
the complex number Z satisfies
Z/(Z+4)= 3+2i
Find Z.
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??
thank you 
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. 
thanks!