One is equal to minus one.

[cguy]

1 = √(1)
= √[(−1).(−1)]
= √[(−1)^(2)]
= [((-1)^2)^0,5]
1 = -1

Where is my mistake?

You're assuming that (x^a)^b == x^(a*b), but this is only true for x >= 0. So you have to order the calculation by the parenthesis (which gives 1==1).

Edit: This is equivalent to what Gorden_R said.