relationship between Gaz and Zim in the 表示する could be accurately described as unfriendly and aloof. Acquaintances at best, neither character has ever expressed anything close to affection for または even a friendly demeanour towards the other. In fact, Gaz has hardly spoken もっと見る than a few lines to Zim, and clearly considers him a vague nuisance rather than an actual threat to Earth.
Their contact throughout the series is very limited. Not unlike Dib's disregard for GIR, Zim often brushes his mortal enemy's little sister off when dealing with the pair of them. It is hinted in Future Dib that he...

I woke up with my wig sticking to my head because of the moister from yesterdays tears.the radio was playing "Gone Forever" によって three days grace."So I'll stay up all night,with these bloodshot eyes while these walls surround me with the story of our life..."i sang along but trailed off. what was i to do now that i knew that i had killed my perfect enemy? my arch enemy? i curled up on the bed, thinking. i listened to the song and wished I could be glad he was gone forever. but i could only find one reason to be happy: he couldn't expose us."and now your gone forever..." sang カップケーキ from downstairs.I...