Negative numbers

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Negative numbers are real numbers that are less than 0. Negative numbers are written with a minus sign "−" preceding the absolute value, e.g., −47. This can be thought of as a shorthand for 0 − 47.

Multiplying a negative number by −1 gives its absolute value, e.g., $|-{\frac {5}{8}}|=(-1)(-{\frac {5}{8}})={\frac {5}{8}}$.

The square of a negative number $x$ is a positive number, and in fact $x^{2}=(-x)^{2}$; but the square root of that negative number is a purely imaginary number of the form $i{\sqrt {|x|}}$, where $i$ is the imaginary unit. For example, $(-49)^{2}=2401$, but ${\sqrt {-49}}=7i$.