CV18

From Exampleproblems

$\sqrt{-8-6i} \,$

Rearranging the coeficient of $i\,$

$\sqrt{-8-6i}=\sqrt{-8-2(3)(1)(i)}\,$

Adding and subtracting 9 on the right hand side, we get $\sqrt{-8-6i}=\sqrt{-8-2(3)(1)(i)+9-9} \,$

Simplifying and readjusting $\sqrt{-8-6i}=\sqrt{1-2(3)(1)(i)-3^{2}} \,$

again rearranging 9 as a multiple of $i\,$

$\sqrt{-8-6i}=\sqrt{1^{2}-2(3i)(1)+(3i)^{2}} \,$

Hence readjusting the values $\sqrt{-8-6i}=\sqrt{(1-3i)^{2}} \,$

Hence the value is $\sqrt{-8-6i}=1-3i\,$