Root Of Complex?

The principal amplitude (or proper amplitude) of i is (Pi/2)

So

i = cis (Pi/2)

Then

i^(1/16) = cis (Pi/32 + k Pi/8) , k = 0 , 1 , 2 , 3 , ......... , 15

The conjugate of cic (x) = cis (2 Pi - x)

Then

The conjugate of i^(1/16) = cis (2 Pi - Pi/32 - k Pi/8) , k = 0 , 1 , 2 , 3 , ......... , 15

= cis (Pi/32)(63 - 4 k) , k = 0 , 1 , 2 , 3 , ......... , 15

This does not equal any of the given values for any of the 16 values of k

$\iota^\frac{1}{16}=cis \frac{\pi}{32}$ $\Rightarrow$ Conjugate Of $i^\frac{1}{16}$ = $cis \frac{-\pi}{32}$ . So the answer is $\boxed{None Of The Options}$ .