## Intermediate Algebra for College Students (7th Edition)

$i$
Note that $i^{21} = i^{20+1}$ RECALL: (1) $a^{mn} = (a^m)^n$ (2) $i^2=-1$ (3) $a^{m+n} = a^m \cdot a^n$ Use rule (3) above to obtain: $=i^{20} \cdot i$ Use rule (1) above to obtain: $=(i^2)^{10} \cdot i$ Use rule (2) to obtain: $=(-1)^{10} \cdot i$ Note that when $-1$ raised to an even power, the result is $1$. Thus, the expression above simplifies to: $= 1 \cdot i \\=i$