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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.

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

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  • $\begingroup$ Thank you, I should have caught that. $\endgroup$ – user27343 Sep 21 '18 at 2:07

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