Author: M Dabbs

Construction to find complex roots of a quadratic

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Move points A and F

A = (2.815441025711368, 0.4503916014126457)
a = OrthogonalLine(A, xAxis)
B = Intersect(a, xAxis)
F = Point(a)
D = Midpoint(F, B)
c = Circle(D, F)
b = OrthogonalLine(A, a)
C' = Mirror(F, b)
d = OrthogonalLine(C', a)
E = Point(d)
e = Segment(F, E)
F_1 = Midpoint(F, E)
f = OrthogonalLine(F_1, e)
g = OrthogonalLine(E, d)
G = Intersect(f, g)
h = Segment(G, E)
loc1 = Locus(G, E)
H, I = Intersect(c, b)
i = OrthogonalLine(H, xAxis)
B' = Mirror(B, i)
k = Circle(B, B')
J, K = Intersect(k, a)
L = Intersect(xAxis, yAxis)
j = Segment(L, K)
l = Segment(L, J)
Z_1 = Intersect(j, a)
Z_2 = Intersect(l, a)