Answer
$1+i$
Work Step by Step
Using $i^2=-1$ and the laws of exponents, the given expression, $
i^8-i^7
,$ is equivalent to
\begin{array}{l}\require{cancel}
(i^2)^4-i^6\cdot i
\\\\=
(i^2)^4-(i^2)^3\cdot i
\\\\=
(-1)^4-(-1)^3\cdot i
\\\\=
1-(-1)\cdot i
\\\\=
1+i
.\end{array}