square roots

the square root of -96 doesn't exist over the real numbers.

 

However over the complex numbers  if you have some number 

 

^{\(-a, ~~~~a>0 \\ \mbox{then }\sqrt{-a} = \sqrt{-1 \times a} = \sqrt{-1}\times \sqrt{a} = \imath \sqrt{a} \\ \mbox{The symbol } \imath \mbox{ also referred to as just }i \mbox{ or in electrical engineering as }j \\ \mbox{stands for }\sqrt{-1} \mbox{ and is a Complex number.}\)}