Question

1=1^(1/2)=[(-1)(-1)]^(1/2)=i* i=-1 , which is contradiction....why?(i=(-1)^1/2)

Answer 1

It is a contradiction because you cannot distribute the (1/2) exponent in the expression [(-1)*(-1)]^(1/2), i.e. [(-1)*(-1)]^(1/2) != [(-1)^(1/2)]*[(-1)^(1/2)].

Answer 2

Keep in mind that the property sqrt(x*y) = sqrt(x)*sqrt(y) only holds if at least one of the two is positive.