# How do you find abs(i^2)?

Apr 16, 2016

$\left\mid {i}^{2} \right\mid = 1$

#### Explanation:

$i$ is the square root of $- 1$, or

$i = \sqrt{- 1}$.

Therefore,

${i}^{2} = - 1$,

simply by the definition of a square root.

Ultimate value (abs) can be thought of as the distance of a certain number from $0$, always as a positive number, so

$\left\mid - 1 \right\mid = 1$

and, by extension,

$\left\mid {i}^{2} \right\mid = 1$