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In mathematics, two points in the Cartesian plane are hyperbolically orthogonal if the slopes of their rays from the origin are reciprocal to one another.
If the points are (x,y) and (u,v), then they are hyperbolically orthogonal if
- y/x = u/v.
Using complex numbers z = x + y i and w = u + v i, the points z and w in C are hyperbolically orthogonal if the real part of their complex product is zero, i.e.
- xu - yv = 0.
If two hyperbolically-orthogonal points form two angles with the horizontal axis, then they are complementary angles.
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