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## Homework Statement

$$\frac{1}{z}+\frac{1}{2-z}=1$$

## Homework Equations

Quadratic-formula and algebra

## The Attempt at a Solution

Been struggling with this one.. I keep getting the wrong answer, but that isn't the worst part, I can live with a wrong answer as long as the math behind it is correct(formulas etc.) .

So this is the culprit:

$$\frac{1}{z}+\frac{1}{2-z}=1

\Rightarrow \frac{z}{z(2-z)}+\frac{z-2}{z(2-z)}=1

\Rightarrow \frac{z+z-2}{2z-z^2+2z-z^2}=1

\Rightarrow \frac{-2}{2z-2z^2}=1

\Rightarrow -2z^2+2z+2=0

\Rightarrow \frac{-2\pm\sqrt{s^2-4*-2*2}}{2*-2}

\Rightarrow \frac{-2\pm\sqrt{-12}}{-4}

\Rightarrow \frac{2\pm4i\sqrt{3}}{4}

\Rightarrow \frac{1\pm2i\sqrt{3}}{2}

\Rightarrow \frac{1}{2}\pm i\sqrt{3}$$

And this is far from correct.. I should have gotten ## 1 \pm i##.

So I must have done some illegal operation(sick with the flu so my brain isn't working 100%..)

Cheers!

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