Solution
= Solution
Since $(1-i)^3=-2-2i$, divide and multiply by the <complex conjugate> of the denominator:
$$
\boxed{\frac{i}{(1-i)^3}=\frac{i(-2+2i)}8=-\frac14-\frac14i.}
$$
Multiplication by $-2-2i$ verifies the result directly.
= Solution
Since $(1-i)^3=-2-2i$, divide and multiply by the <complex conjugate> of the denominator:
$$
\boxed{\frac{i}{(1-i)^3}=\frac{i(-2+2i)}8=-\frac14-\frac14i.}
$$
Multiplication by $-2-2i$ verifies the result directly.