I am having hard time finding it, the method for finding orthocentre and circumcentre we use in coordinate geometry won't work here if complex number are not given in form of a+ib.
2026-03-27 18:27:47.1774636067
Find complex number representing circumcentre and orthocentre of a triangle with vertices represented by complex number z1, z2, z3?
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If $R_C$ be the circumradius and $z$ be the complex number representing the circumcentre then we have the condition: $$|z - z_1| = |z - z_2| = |z - z_3| = R_C$$ Again, if $z'$ be the orthocentre then it satisfies the condition: $$Re(\frac {z' - z_1}{z_2 - z_3}) = Re(\frac {z' - z_2}{z_3 - z_1}) = Re(\frac {z' - z_3}{z_1 - z_2}) = 0$$ I hope it helps.