How to plot this complex division? $$ \sqrt{\frac{a^2+(b-1)^2}{a^2+(b+1)^2}}=2 $$
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The plot of $\sqrt{\frac{a^2+(b-1)^2}{a^2+(b+1)^2}}=2$ is the following:
Work out $a^2+(b-1)^2$ and $a^2+(b+1)^2$. This will give: $$\frac{a^2+(b-1)^2}{a^2+(b+1)^2} = \frac{1-4b}{a^2+b^2+2 b+1}$$
This would make it easier to solve.
user112167
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1Link only answers are discouraged. It's better if you post the picture directly. – Git Gud Dec 15 '13 at 17:02
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Sorry, placed the picture. – user112167 Dec 15 '13 at 17:04
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Thats what i did, but i do not understand how they solved this equation, how they got the solution a=4/3 and b=-5/3 – user115961 Dec 15 '13 at 17:04
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@user115961: Why not simplify your equation? You'll get an simple equation which represents the circle above. – mathlove Dec 15 '13 at 17:08
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Squaring the given equality you can arrive at
$$a^2+b^2+\frac{10}{3}b+1=0. ~~(*)$$
Consider now the $(a,b)$-plane: can you recognize the locus of points which satisfy $(*)$? Looking at its discriminant you should be able to identify such locus as a circle.
To draw it, start to find the points of intersections with the coordinate axis, for example.
Avitus
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