Performing Arithmetic with Complex Numbers

The square root of a negative number is an imaginary number. We get the same value as if we were to take the square root of the corresponding positive number, however, we have to include the imaginary unit, $i,$ after taking the square root. $$\sqrt{\text{-}4}=\sqrt{4}\cdot i=2i$$

In the same way as in the previous exercise, the square root of a negative number is equal to the square root of the corresponding positive number, and then multiplied by the imaginary unit: $$\sqrt{\text{-}9}=\sqrt{9}\cdot i=3i.$$

The definition of the imaginary unit is $I^2=\text{-}1,$ which can also be written as $i=\sqrt{\text{-}1}.$ We can also reason as in previous exercises and get $$\sqrt{\text{-}1}=\sqrt{1}\cdot i=i.$$

Proceed in the same way as previously and take the square root of the corresponding positive number, and then multiply it by $i$: $$\sqrt{\text{-}100}=\sqrt{100}\cdot i=10i.$$