The ellipse seemed rather simple: Defining the equation of an ellipse in the complex plane
But Wolfram won't graph it with equal axes. http://www.wolframalpha.com/input/?i=abs{%28x%2Biy%29}%2Babs{%28x%2Biy%29}%3D1
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1I don't really understand what you want. If I follow the title, the equation of a circle of centre $a+ib$ and radius $r$ is given by $|z-(a+ib)|=r$. Is it what you want ? – Surb Jun 22 '16 at 12:24
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@Surb graphing the circle = harder than typing the equation in Wolfram. – User3910 Jun 22 '16 at 12:25
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What do you mean by graphing ? you want to draw it ? – Surb Jun 22 '16 at 12:26
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@Surb I was trying to get wolfram alpha to graph it without success. – User3910 Jun 22 '16 at 12:28
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@Surb yes I mean draw = graph. – User3910 Jun 22 '16 at 12:29
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is there a question ? – mercio Jun 22 '16 at 12:43
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You might be better trying:
$$z=e^{i\theta}$$ or $$z=\cos(\theta)+i\sin(\theta)$$
These are derived from Euler's famous formula:
$$e^{i\theta}=\cos(\theta)+i\sin(\theta)$$
They more naturally plot the unit circle in the complex plane.
it's a hire car baby
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Wolfram doesn't graph you equations. Though image searching them yeilds the desired circles. – User3910 Jun 22 '16 at 20:20
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It graphs the sine and cos functions separately and not plotted in the real plane! – it's a hire car baby Jun 22 '16 at 21:18