What is (√-1)²?

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Answer 1 · 2017-10-21T10:07:46

-1

$\sqrt{- 1} = i$ $sqrt(-1) = i$

${(\sqrt{- 1})}^{2} = i^{2} = i \cdot i = \sqrt{- 1} \cdot \sqrt{- 1} = - 1$ $(sqrt(-1))^2= i^2=i*i= sqrt(-1)*sqrt(-1)= -1$

Answer 2 · 2017-10-21T10:14:45

${(\sqrt{- 1})}^{2} = - 1$ $(sqrt(-1))^2 = -1$

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

$\sqrt{- 1}$ $sqrt(-1)$ denotes the principal square root of $- 1$ $-1$ which is a square root of $- 1$ $-1$ .

Therefore its square must be $- 1$ $-1$ .