Impossible, Imaginary, Useful Complex Numbers. Ch. 17 Chris Conover & Holly Baust. SOLVE. Solve the equation x 2 +2x+7 Use the quadratic formula. Solve on the calculator using a+bi mode. Overview. Introduction Cardano Bombelli De Moivre & Euler Berkeley, Argand, and Gauss Hamilton
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Chris Conover & Holly Baust
Solve on the calculator using a+bi mode
Works for many cubics….but WAIT!
The process of dealing with the square root of negative one is “as refined as it is useless.”
“And although to many this will appear an extravagant thing, because even I held this opinion some time ago, since it appeared to me more sophistic than true, nevertheless I searched hard and found the demonstration, which will be noted below. ... But let the reader apply all his strength of mind, for [otherwise] even he will find himself deceived.”
cos(x+y) = cos(x)cos(y)-sin(x)sin(y)
(cos(x)+isin(x))n = cos(nx)+isin(nx)
q = w+xi+yj+zk, where i, j, and k are all different square roots of -1 and w, x, y, and z are real numbers