The Imaginary Unit

The imaginary unit is defined by i2=-1. i^2=\text{-} 1. From this definition, it follows that -1=i,\sqrt{\text{-} 1}=i, which allows the square root of any negative number to be found. What results is called an imaginary number. Once ii replaces the negative sign, the square root of the remaining positive number can be evaluated as usual.

-a=a-1=ai\sqrt{\text{-} a} = \sqrt{a} \cdot \sqrt{\text{-} 1} = \sqrt{a} \cdot i
 \ \quad Condition: a>0a > 0

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