প্রমান, -১ = ১

 ......................  🅿︎🆁︎🅾︎🆅︎🅴︎  [ -1 = 1]  .....................

(-1)^2 = 1

Or, 2log (-1)= log 1 = 0 

Or, log (-1) = 0

Or, -1 = exp(0)

Therefore,  -1= 1

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Again, 

Let, exp(x) = -1

Square on both side, 

Or, exp(2x) = 1

Or, 2x = 0

Or, x = 0

Or, exp(x) = exp (0)

But,  exp(x) = exp(0) and exp (0) = 1

Therefore, -1= 1

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Again,

√-1 = √-1

Or,  √(-1/1) = √(1/-1)

Or, √-1/ √ 1 = √1 / √-1

Or, (√-1)^2 = (√1)^2

Therefore,  -1 = 1

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We know, 

√(a-b) = i √(b-a) --------(1)

and,  

√(b-a) = i √(a-b) ---------(2)

Multiplying (1) and (2), 

√(a-b)√(b-a) = i^2 √(b-a)√(a-b)

Or, 1 = i^2

Therefore,    1 = -1