The Theory of the Imaginary in Geometry

Cover The Theory of the Imaginary in Geometry
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__ = L rp. - A.G' BA 1 GB' 1 Therefore _._ _ = _i.
Trigonometry of the Imaginary 87 Analytical verification of the fact that the sum and difference formulae hold for a real and an imaginary angle.
Let c, a + ib, be the coordinates of any point P. Let OQ = c, NQ = a and NP = ib.
Drop PM perpendicular to ON, and MK perpendicular to OX. Let QOJY=a and MOP=p ( , so that NPM=a. If sin (a + ft) = sin a cos ft + cos a sin ft, then y (p; (M) N rx fa) * v a (C) c !
X Z + 4& ivWc 2 +;& Va 2 + c 2 Va 2 +
...o 2 Va 2 + c 2 ' vW(

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