I must be doing something wrong in the following question and would appreciate clarification:
Given that $i^2$= -1, and that k is a positive integer, what is the value of $i^{4k+2}$?
My answer:
$i^{4k+2}$ = $i^{4k}$+$i^2$
$i^{4^{k}}$+ $i^2$
$i^2$=-1, $i^4$=1
$1^k$=1 + $i^2$ = 0
The answer should be -1.
Best Answer
This is wrong $$i^{4k+2}=i^{4k}+i^2$$ This is right $$i^{4k+2}=i^{4k}\cdot i^2=-i^{4k}=-(i^4)^k=-1$$