# Imaginary number/exponent rules misconception

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 $$i^{4k+2}$$?

$$i^{4k+2}$$ = $$i^{4k}$$+$$i^2$$

$$i^{4^{k}}$$+ $$i^2$$

$$i^2$$=-1, $$i^4$$=1

$$1^k$$=1 + $$i^2$$ = 0

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