# What is (√-1)²?

Oct 21, 2017

-1

#### Explanation:

$\sqrt{- 1} = i$

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

Oct 21, 2017

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

#### Explanation:

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 $- 1$.