Question

express sqrt-75 in terms of i.

Answer 1

5i(root(3))

Answer 2

Important to remember that a root of a negative is not expressed in the way we would with a non negative. This is one reason that (the invention of) i is so useful.
Ok here we go
√-75 could also be written √-(3 x 5 x 5)
Which in turn could be written
√-(3 x 25) or √-25 x √3 or alternatively √25 x √-3
You should use the second option because we can write √-25 as 5i and take it outside.
Giving 5i √3 as your answer

Answer 3

first root : +i5sqrt3
second root : -i5sqrt3