I would like to apply this theorem to a triangle on the unitcircle: Let P be a point on the unit circumcircle of triangle ABC. The equation of its Simson line is:
$$2abc\overline{z}-2pz+p^2+(a+b+c)p-(bc+ca+ab)-\frac{abc}{p}=0 $$
Ive tried with $$\Delta ABC $$ for $$a=-i,b=1,c=i,p=\frac{i}{2}-\frac{1}{2}$$
substituting in the theorem gives $$-2 \overline{z}+(1-i)z-\frac{3}{2}-4i=0$$ then $$-2(x-yi)+(1-i)(x+yi)=\frac{3}{2}+4i$$ gives $$-x+y+i(3y-x)=\frac{3}{2}+4i$$ resulting in: $$x=\frac {5}{4},y=-\frac{1}{4}$$
How do I form this into a line?