Simplify.
-$\mathrm { i } ^ { 23 } - \mathrm { i } ^5$
A) $- 2 i$
B) $2 \mathrm { i }$
C) 0
D) $- 2$

Question

Quizplus · Accepted Answer

$\mathrm { i } ^ { 23 } - \mathrm { i } ^5$ simplifies to $-2i$ because $\mathrm { i } ^ { 23 }$ and $\mathrm { i } ^5$ both simplify to $-i$, and $-i - (-i) = -2i$. Powers of $i$ cycle through $i, -1, -i, 1$, so $\mathrm { i } ^ { 23 }$ and $\mathrm { i } ^5$ (both 3 more than a multiple of 4) equal $-i$.

Simplify - i23−i5\mathrm { i } ^ { 23 } - \mathrm { i } ^5i23−i5

Simplify
- $\mathrm { i } ^ { 23 } - \mathrm { i } ^5$