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!

Calculuscomplex 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

Calculuscomplex 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

Calculuscomplex 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.

Calculuscomplex numbers  Anne?, Thursday, March 13, 2008 at 9:52am
thanks!
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