text: riddle- proof that  1=-1? try this out on paper as it would be easier to read & understand........ we start with- -1=-1 =>1/(-1)=-1/1 =>[1/(-1)]^1/2=[(-1/1)]^1/2 =>[(1)^1/2]/[(-1)^1/2]=[(-1)^1/2]/[(1)^1/2]  multiplying both sides by [(1)^1/2]*[(-1)^1/2] & voila--> -1=1 hello  step 1:  1/(-1)=-1/1  is ok step 2: [1/(-1)]^1/2=[(-1/1)]^1/2  is ok this is equal to:  i=i  step 3: [(1)^1/2]/[(-1)^1/2]=[(-1)^1/2]/[(1)^1/2] is wrong in this step is where you get:  1/i=i/1 1/i=i 1=i^2 1=-1  as you see, no need to multiply and cancel to get same result you got.  the trick was to rearange values in step 1, and later split the roots on step 3.