Complemento translates to "complement" in English. It refers to something that completes or makes perfect.
In "La Otra Parte De Ti," the word is used to describe a person's ideal partner, the missing piece that makes them whole. The lyrics speak of "la mitad de tu amor tu complemento" (the half of your love, your complement) and "la mitad de tu ser a quien debes tener" (the half of your being whom you should have), emphasizing the idea of finding one's perfect match.
Have you ever wondered who that "other part of you" is? La Maquinaria Norteña explores this idea in "La Otra Parte De Ti." The song talks about how a sincere friend, a fleeting love, or even someone who controls your heart could be that missing piece. The singer believes he could be that person for you, saying, "puedo ser yo" [I can be me]. He knows this because he's ready to fall in love with you, promising to correct things in his life and always be there.
He's serious about this commitment! He even says, "mil infiernos vivientes de esperaron si me miente y que un rayo me para retar se olvidó tu amor" [a thousand living hells awaited me if I lie and may a lightning bolt stop me from challenging your love]. It's a pretty intense way to say he's all in! He sees himself as your complement, the other half of your being that you're destined to find sooner or later. He's hoping that major surprise, that perfect gift, turns out to be him.