Question

Evaluate `(sqrt(-1))/(sqrt(-6)sqrt(-1))`?

Answer 1

`sqrt(-1)/(sqrt(-6)sqrt(-1)) = -sqrt(6)/6 i`

Explanation:

If `n < 0` then `sqrt(n) = sqrt(-n) i` where `i` is the imaginary unit.

So we find:

`sqrt(-1)/(sqrt(-6)sqrt(-1)) = 1/sqrt(-6) = 1/(sqrt(6)i) = (sqrt(6)i)/(6i^2) = -sqrt(6)/6 i`