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

We can find the value of a power of i by using ${i}^{2} = - 1$.
${i}^{5} = {i}^{2} \cdot {i}^{2} \cdot i = \left(- 1\right) \cdot \left(- 1\right) \cdot i = i$
${i}^{6} = {i}^{2} \cdot {i}^{2} \cdot {i}^{2} = \left(- 1\right) \cdot \left(- 1\right) \cdot \left(- 1\right) = - 1$