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)
|
