Solution
= Solution
Integer powers of $i$ repeat with <period> four. Thus $i^{-5}=i^{-4}i^{-1}=1/i=-i$, and
$$
\boxed{\Re z=0,\qquad\Im z=-1.}
$$
This negative integer power is single-valued and does not require a logarithm branch.
= Solution
Integer powers of $i$ repeat with <period> four. Thus $i^{-5}=i^{-4}i^{-1}=1/i=-i$, and
$$
\boxed{\Re z=0,\qquad\Im z=-1.}
$$
This negative integer power is single-valued and does not require a logarithm branch.