Question

Simplify the expression.

i^313

Answer 1

divide 313 by 4 and take the integer remainder

Answer 2

4 goes on to 312 evenly so the remainder is 1 in this case.
therefore \(i^{313}=i^1=i\)
pattern is
\[i^0=1\]
\[i^1=i\]
\[i^2=-1\]
\[i^3=-i\]
\[i^4=1\] and so on

Answer 3

ok so when i divided 313 by 4 i got 78.25 would i round that to 8?

Answer 4

it is the remainder you are looking for

Answer 5

and then divide that by 4 again?

Answer 6

by which i mean the integer remainder.
4 goes in to 313 78 times with a remainder of 1 so you are only concerned with the 1

Answer 7

i.e. \(313=78\times 4+1\) ignore the first part, work only with the 1

Answer 8

So you would divide 78 by 4?