The word "气死" is formed by combining the character "气", which in this context means "anger" or "to make angry", with the character "死", meaning "to die". This creates a verb-complement structure where "气" indicates the action of causing anger, and "死" serves as a resultative complement, implying that the anger is so severe it leads to a state akin to death, thus idiomatically conveying the meaning of being extremely angry or furious.