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

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): square root

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