If $\displaystyle z=x+yi$ find the values of $\displaystyle x$ and $\displaystyle y$ such that $\displaystyle \frac{z-1}{z+1}=z+2$

Thanks for your help!

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- Jul 30th 2009, 12:36 AMStroodleComplex number question
If $\displaystyle z=x+yi$ find the values of $\displaystyle x$ and $\displaystyle y$ such that $\displaystyle \frac{z-1}{z+1}=z+2$

Thanks for your help! - Jul 30th 2009, 12:52 AMred_dog
$\displaystyle \frac{x-1+yi}{x+1+yi}=x+2+yi\Rightarrow x-1+yi=x^2+3x-y^2+2+i(2xy+3y)\Rightarrow$

$\displaystyle \Rightarrow\left\{\begin{array}{ll}x^2+3x-y^2+2=x-1\\2xy+3y=y\end{array}\right.\Rightarrow\left\{\be gin{array}{ll}x^2-y^2+2x=-3\\2y(x+1)=0\end{array}\right.$

Now, you have to solve the system. Can you do that? - Jul 30th 2009, 12:57 AMGamma
- Jul 30th 2009, 12:59 AMStroodle
Awesome. THanks for your help guys

- Sep 5th 2009, 10:50 PMMr Smith
- Sep 5th 2009, 10:57 PMProve It