The recording's backing track uses conventional acoustic drums, acoustic piano, and electric bass guitar, however the distinctive lead parts are performed on violin,viola and heavily flanged and reverberated analogue monosynth, an unusual combination in popular music.
Lyrically, the song alludes to a psychological complex, expressing a paranoia that might have been directed at critics, fans, stalkers or false friends, depending on one's point of view:
- Please keep them away
- Don't let them touch me
- Please don't let them lie
- Don't let them see me
A BBC Radio 1 review panel speculated that this song was "the first electronic ballad", although this is untrue, as it post-dates recordings such as "Hiroshima Mon Amour" by Ultravox and "Neon Lights" by Kraftwerk by a couple of years.
Numan rarely performed "Complex" in concert throughout the '80s and '90s, with versions appearing on the recently re-released and expanded 1980 recordings captured on Living Ornaments '80, as well as the Micromusic video from his final Wembley Arena concert in 1981 and its CD counterpart Living Ornaments '81. He revived the song on stage in September 2003, as captured in the "Hope Bleeds" DVD and CD.