Today I tried to understand the formulas for complex geometry couldn't find the proofs. Where can I find the proofs?(especially perpendicularity, concyclic criteria, directed angles and triangles explanations). Also, I tried to use the formula $A,B,C,D $ are concylic iff $\frac{b-a}{c-a} ÷ \frac{b-d}{c-d} \in \mathbb{R}$ to prove the statement below, but I obtained the value of $\frac{4i+1}{5}$. Are the points just not concyclic? Prove that $ABCD$ is cyclic, where $A (3 - 2i), B (2-i), C (-2 + 3i), D (1 - 2i)$
2026-05-16 16:10:03.1778947803
Complex geometry formulas
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Note that point $B$ is on $\overline{AD}$. The graph is below (in the Cartesian, not complex plane):
No matter how you connect the points, the "quadrilateral" is equivalent to either a triangle or two triangles with one common point. Since all triangles are cyclic, this "quadrilateral" is cyclic.
-FruDe