Question

Part 1: Explain, in complete sentences, the relationship between radicals and complex numbers.

Answer 1

in complex numbers there is a convienient relationship -1 = i^2

so when working with radicals and having a negative value then the negative can be replaces by i^2


e.g. \[\sqrt{-20} = \sqrt{20i^2}\]

now you can simplify the radical by removing the squares...

\[\sqrt{20i^2} = \sqrt{4i^2 \times 5} = 2i \sqrt{5}\]

Answer 2

Thank you very much.