Posted by **Anne** on Thursday, March 13, 2008 at 7:11am.

the complex number Z satisfies

Z/(Z+4)= 3+2i

Find Z.

please help thx!

- Calculus--complex numbers -
**drwls**, Thursday, March 13, 2008 at 8:15am
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

- Calculus--complex numbers -
**Anne---?**, Thursday, March 13, 2008 at 8:32am
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

- Calculus--complex numbers -
**drwls**, Thursday, March 13, 2008 at 9:41am
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.

- Calculus--complex numbers -
**Anne---?**, Thursday, March 13, 2008 at 9:52am
thanks!

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