SOLUTION: My teacher proved that -1 = 1, homework is to find out what is wrong with the proof. I cant do it. Help, thanks Mick. -1/1=1/-1 ....Take the square root of both sides;- (-

Question 181401: My teacher proved that -1 = 1, homework is to find out what is wrong with the proof. I cant do it. Help, thanks Mick.
-1/1=1/-1
....Take the square root of both sides;-
(-1/1)^.5=(1/-1)^.5
....Take the square root of each term;-
(-1)^.5/(1)^.5=(1)^.5/(-1)^.5
....Sq Root -1 = i Sq Root 1 = 1;-
i/1=1/i
....Cross multiply;-
i^2=1^2
....Sq Root i is -1 and SqRoot 1 is 1;-
-1=1
....QED
Thanks for any help again.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The problem is that you make the claim that

which is not exactly true. In fact i is variously defined as

or as the root of the equation

. In fact,

, and not considering both branches is what gets you into absurdity.

John

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