Question

simplify i^13
i^53
i^5

Answer 1

divide the exponent by 4 and take the integer remainder

Answer 2

so first one is
\[i^{13}=i^1=i\]

Answer 3

\[i^p=i^{4 \cdot q+r}\]

just divide p each time by 4 and the remainder will be number that you really want to look at

Answer 4

second one is
\[i^{53}=i^1=i\]

Answer 5

i
i
i

Answer 6

and the last one is...
\[i^5=i^1=i\] the i's have it

Answer 7

since
\[i^p=i^{4 \cdot q+r}=(i^4)^qi^r=1^qi^r=1i^r=i^r\]

Answer 8

ooh fancy division algoriddim!

Answer 9

i
i
i