Assuming that
( i ) = (1/2)
+ i (1/2)
we can square both sides to get
i = [ (1/2) + i (1/2)
]^{2}
i = [ (1/2) + 2(1/2) i + (1/2) i^{2} ]
i = [ (1/2) + i + (1/2) (-1) ]
i = i (which is a true statement)

This is not a proof, but simply evidence that the formula is correct.