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Calculus--complex numbers

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the complex number Z satisfies
Z/(Z+4)= 3+2i

Find Z.

please help thx!

  • Calculus--complex numbers - ,

    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 - ,

    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 - ,

    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 - ,

    thanks!

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