i dont know how those horrible things are related to x rays but i can answer your question.

SIMPLY USE e^(j theta)= cos theta + j sin theta

like the first one, i am doing say....

1 + cos(-pi) +j sin (-pi) +cos (-2 pi) +j sin(-2 pi) +cos (- pi) + j sin (-pi)

remembering cos(-theta)=cos theta and sin (- theta)=- sin theta .....cos is even and sin is odd function

i get 1-1+1-1=0

i think u can easily do the rest.

please tell how these things are related to x rays?

do they explain bremmstralung or characteristics?