Help Me I don’t get it

i^11 + i^111

Here's another method you might find easier :

Note i^2  = -1

i^11  =  i^10 * i   =  (  i^2 )^5  * i   =  (-1)^5 * i

And  - 1 raised to an odd power = -1

So....we have    (-1) * i   = - i

Likewise

i^111  =  i^110 * i   =   (i^2)^55 * i  =  (-1)^55 * i   =  -1 * i  =  -i

So

i^11 + i^111  =

-i  + -i  =

-2i