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The question is $$\left|z-1-i\right|=2$$

And my working has gone like this $$\left|z-1-i\right|^2=4\Rightarrow\left|\left(x-1\right)+i\left(y-1\right)\right|^2=4\Rightarrow\left(x-1\right)^2+\left(y-1\right)^2=4$$ This then means that the centre $z_0$ is $\left(1,1\right)$. So would this then mean that the inverse points, $z_1,z_2$ satisfy $$\left(z_1-\sqrt{2}\right)\left(z_2-\sqrt{2}\right)=4$$ Which would then mean that $$z_1=4+\sqrt{2},\quad z_2=1+\sqrt{2}.$$ What would the equation in inverse form be?

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    What do you mean by "the pair of inverse points"? Where are you getting that $\sqrt{2}$? – 2017-02-16
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    $$\sqrt{2} = \sqrt{1^2+1^2}$$ which is the distance from the center of the circle $z_0$ to the origin. inverse because one of $z_1$ and $z_2$ is inside the circle and one is outside. I don't know if I'm right which is why I asked for help on here? – 2017-02-16
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    I'm trying to figure out what the question is. What are $z_1$ and $z_2$ supposed to be? – 2017-02-16

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