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Use the principal complex logarithm at each stage of the nested complex exponentiation. Since $\mathrm{Log}i=i\pi /2$,This inner value is positive real, so its principal complex logarithm is $-\pi /2$. ConsequentlyOne must retain the parentheses: complex exponentiation is not associative. If all complex logarithm branches are allowed, the inner values are $e^{-\pi /2-2\pi k}$. Taking the outer logarithm with an independent integer branch index $\ell$ yields $\exp [-i\pi /2-2\pi ik-2\pi \ell ]=-i{e}^{-2\pi \ell }$. Thus the complete multivalued set is $\{-i{e}^{-2\pi \ell }:\ell \in \mathbb{Z}\}$, and the boxed answer selects its principal evaluation.

The inner power takes the values $r_k=e^{-(\pi /2+2\pi k)}$. For each such real exponent, all values of the outer complex exponentiation are obtained from all complex logarithm values of its base $i$:Writing ${\Theta }_{k,m}=(\pi /2+2\pi m)e^{-(\pi /2+2\pi k)}$, the answer isAll values lie on the unit circle. The principal choice is $k=m=0$, giving $\cos [(\pi /2)e^{-\pi /2}]+i\sin [(\pi /2)e^{-\pi /2}]$. In particular the two nestings in parts (i) and (ii) are different: complex exponentiation is not associative.