a = 1
cos x = sin yb = 1
r = root 2
cos x = (a + r) . 1/(|a||r|)
= sin y
This proves that 1/root 2 = "i" = cos x = sin y
Discoursive proof
– equivalences, unit vectors
cos^2 = sin^2 = ½ = -1
cos^2 + sin^2 = 1
cos = sin
(root 2) cos x = 1
(root 2) cos y = 1
From the laws of vectors
Equivalent vectors are:
-2 = 2
-(root 2) = root 2
-1 = 11 + 1 = root 2
root 2 = r = -i
-1 + 1 = (+i)(-(-i)) = (1/root 2).(1/root 2) = ½ = i^2
All proved on another page.....
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