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Complexity
(Math | Miscellaneous | Complexity | sqrt(i))

 

Rationale that sqrt( i ) = sqrt(1/2) + i sqrt(1/2)

Assuming that
  sqrt( i ) = sqrt(1/2) + i sqrt(1/2)
we can square both sides to get
  i = [ sqrt(1/2) + i sqrt(1/2) ]2
  i = [ (1/2) + 2(1/2) i + (1/2) i2 ]
  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.

  
 
  

 
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