Question

i^34

Answer 1

Can you tell me what the remainder is when divide 34 by 4?

Answer 2

Always divide the exponent by 4 and see what the remainder is...

Answer 3

so then you will have
\[i^R\]
where R is the remainder
@Luis Rivera We have a new code of conduct. I'm trying to get people to know about it. So one of the things it says is to not just post the answer.

Answer 4

http://openstudy.com/code-of-conduct

Answer 5

i = sqrt(-1)
i^2 = -1
i^3 = -i
i^4 = i^2*i^2 = -1*-1 = 1
keep doing this and notice that every multiple of 4 the answer is 1
for example i^12=1, i^16=1, etc.
closest number 34 that is a multiple of 4 is 32.
so i^32=1
but i^34 = i^32*i^2 = 1*-1=-1

Answer 6

\[i^{4(Q)+R}=(i^4)^Q i^R=(1)^Q i^R=1 \cdot i^R=i^R\]