Given four complex numbers $A, B, C, D$ interpreted as points on the plane, how can I calculate the number that represents the intersection of the lines formed by $A, B$ and $C, D$?
Given the cartesian coordinates of four points, how to calculate the interection of two lines they form?
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geometry
complex-numbers
analytic-geometry
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0Assuming $\arg(B-A)\neq\arg(D-C)$ of course... – 2012-01-08
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0@J.M. Of course. This possibility is ruled out. – 2012-01-08
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0*Mathematica* says: $$\frac{(A-B)\Re(D\Im C-C\Im D)+(C-D)\Re(A\Im B-B\Im A)}{\Re((A-B)\Im(C-D)-(C-D)\Im(A-B))}$$ – 2012-01-08
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0@J.M. Oh yeah. That looks good. THank you! BTW, is there a solution that use the $r,\vartheta$ representation instead? – 2012-01-08
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0@J.M. Could you please provide the Mathematica input that you used to generate your equation: (A−B)R(DJC−CJD)+(C−D)R(AJB−BJA)R((A−B)J(C−D)−(C−D)J(A−B)) I imagine you used Solve[..], but I'm wondering how you told Mathematica to split up the complex numbers like that Thanks – 2012-04-05
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0@tlatev: I don't have *Mathematica* with me at the moment, but if memory serves, I used Cramer's rule and some massaging with `ComplexExpand[]` and `Simplify[]` in all the right places... – 2012-04-10