# How do I find the value of a given power of i?

##### 1 Answer
Sep 26, 2014

We can find the value of a power of i by using ${i}^{2} = - 1$.

Let us look at some examples.

${i}^{5} = {i}^{2} \cdot {i}^{2} \cdot i = \left(- 1\right) \cdot \left(- 1\right) \cdot i = i$

${i}^{6} = {i}^{2} \cdot {i}^{2} \cdot {i}^{2} = \left(- 1\right) \cdot \left(- 1\right) \cdot \left(- 1\right) = - 1$

I hope that this was helpful.