Concept

The Imaginary Unit

The imaginary unit is defined by $i^2=\text{-} 1.$ From this definition, it follows that $\sqrt{\text{-} 1}=i,$ which allows the square root of any negative number to be found. What results is called an imaginary number. Once $i$ replaces the negative sign, the square root of the remaining positive number can be evaluated as usual.

$\sqrt{\text{-} a} = \sqrt{a} \cdot \sqrt{\text{-} 1} = \sqrt{a} \cdot i$

$\ \quad$ Condition: $a > 0$