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.


1 Answer 1


This is wrong $$i^{4k+2}=i^{4k}+i^2$$ This is right $$i^{4k+2}=i^{4k}\cdot i^2=-i^{4k}=-(i^4)^k=-1$$

  • $\begingroup$ Thank you, I should have caught that. $\endgroup$
    – user27343
    Sep 21, 2018 at 2:07

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.