Question

How do I solve problems like this
`{i}^(13)`

Answer 1

`i^(13)=(\sqrt[2]{-1})^(13)=((-1)^{(1)/(2)})^(13)=(-1)^{(13)/(2)}=((-1)^(13))^{(1)/(2)}=(-1)^{(1)/(2)}=\sqrt[]{-1}=i`
`i^4=(\sqrt[]{-1})^4=(-1)^{(4)/(2)}=(-1)^2=1`

when we power the number i to a odd number, we obtain the same i, but when we power i to a even number we obtain 1 instead.