What is (√-1)²?

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Answer 1 · 2017-10-21T10:07:46

-1

#sqrt(-1) = i#

#(sqrt(-1))^2= i^2=i*i= sqrt(-1)*sqrt(-1)= -1#

Answer 2 · 2017-10-21T10:14:45

#(sqrt(-1))^2 = -1#

By definition a square root of a number #x# is a number #y# such that #y^2 = x#.

#sqrt(-1)# denotes the principal square root of #-1# which is a square root of #-1#.

Therefore its square must be #-1#.