Definition:Square Root/Negative Real

Definition
Let $x \in \R_{< 0}$ be a (strictly) negative real number.

Then the square root of $x$ is defined as:


 * $\sqrt x = i \paren {\pm \sqrt {-x} }$

where $i$ is the imaginary unit:
 * $i^2 = -1$

Hence:
 * $\sqrt{-1} = i$

Also see

 * Definition:Complex Square Root