# How do you simplify i^19?

Nov 10, 2015

${i}^{19} = {i}^{3} = - i$

#### Explanation:

There are only four solutions when i is raised to a positive integer:

${i}^{1} = i$
${i}^{2} = - 1$
${i}^{3} = - i$
${i}^{4} = 1$

Find the equivalent exponent by dividing the exponent by 4 , then the remainder will be the equivalent exponent.

$\frac{19}{4} = 4$ with a remainder of 3

Answer: ${i}^{3} = - i$

hope that helped