I was looking for a description of how to represent complex conditions (geometrically). However I googled it and I don't find anything. I was looking for a good summary of the equation of circle, an ellipse, etc. Does anyone know where can I find it?
Asked
Active
Viewed 63 times
0
-
Related: http://math.stackexchange.com/questions/481582/equation-of-ellipse-hyperbola-parabola-in-complex-form – Sep 24 '16 at 10:19
1 Answers
0
As regards conics take a look here: Equation of ellipse, hyperbola, parabola in complex form
Moreover, if you have a curve in the complex plane given by the equation $f(x,y)=0$, you can find a complex representation in terms of $z,\bar z$, by letting $x=\frac {z+\bar z}{2}, y=\frac {z-\bar z}{2i}$.
Try with the equation of the line $ax+by=c$. It follows that all lines in $\mathbb C$ can be written as $$\alpha z + \bar\alpha \ \bar z + \beta = 0$$ where $\alpha \in \mathbb C$, $\beta \in \mathbb R$.
