# How do you simplify i^28?

Mar 20, 2016

${i}^{28} = 1$

#### Explanation:

We will use the following:

• ${i}^{4} = i \cdot i \cdot i \cdot i = {i}^{2} \cdot {i}^{2} = - 1 \cdot - 1 = 1$
• ${a}^{b c} = {\left({a}^{b}\right)}^{c}$

With these, we have

${i}^{28} = {i}^{4 \cdot 7} = {\left({i}^{4}\right)}^{7} = {1}^{7} = 1$