# How do you simplify i^123458?

Factor out ${i}^{4}$
Since $i = \sqrt{- 1}$ then ${i}^{4} = {\left({i}^{2}\right)}^{2} = 1$. "i" to a power of any multiple of four ( i^4,i^8,i^16,...) is 1 , so factor out i to the power that is the next lower multiple of four, in this case 123456.
${i}^{123458} = {i}^{123456} \cdot {i}^{2} = 1 \cdot {i}^{2} = {\left(\sqrt{- 1}\right)}^{2} = - 1$