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[10470] by "FARINA00" (ppp-112-29.30-151.libero.it) on Sat 30 Mar 2002 04:26:24 [ reply ]

let x = pi. cos(pi) = -1, sin(pi) = 0
so e^(i.pi) = cos(pi) + i.sin(pi)
= -1 + 0
and so e^(i.pi) = -1

FAMOUS FIVE!!!!
0, 1, e, pi, i

e^(i.pi) + 1 = 0

LET MANY OTHER THINGI
z = cos(x) + i.sin(x)
Then dz/dx = -sin(x)+i.cos(x)
= i{cos(x)+i.sin(x)}
= i.z

So dz/z = i.dx intergrate
ln(z) = i.x + const. When x=0, z=1 so const=0
ln(z) = i.x

z = e^(i.x)

So cos(x) + i.sin(x) = e^(i.x)

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