# How do you simplify i^100?

Dec 19, 2015

${i}^{100} = 1$

#### Explanation:

${i}^{100} = {\left({i}^{2}\right)}^{50} = {\left(- 1\right)}^{50} = {\left({\left(- 1\right)}^{2}\right)}^{25} = {1}^{25} = 1$

Dec 19, 2015

$1$

#### Explanation:

Even powers of $i$ are equal to $1$

Odd powers of $i$ are equal to plus or minus $i$
The signs alternate