What is the conjugate of $\displaystyle \frac{\ -2}{i^3}$?
To find the conjugate of any complex number, replace i with -i. You could "rationalize the denominator" first, as "a tutor" did:
$\displaystyle \frac{-2}{i^3}= -2i$ and then its conjugate is $\displaystyle -2(-i)= 2i$. Or you can immediately write that the conjugate is $\displaystyle \frac{-2}{(-i)^3}= \frac{2}{i^3}$. If you were then to multiply both numerator and denominator by i you would again get $\displaystyle \frac{2i}{i^4}= \frac{2i}{(i^2)^2}= \frac{2i}{(-1)^2}= 2i$.