The Collaborative International Dictionary of English v.0.48:

Complex \Com"plex\ (k[o^]m"pl[e^]ks), a. [L. complexus, p. p. of
   complecti to entwine around, comprise; com- + plectere to
   twist, akin to plicare to fold. See Plait, n.]
   1. Composed of two or more parts; composite; not simple; as,
      a complex being; a complex idea.
      [1913 Webster]

            Ideas thus made up of several simple ones put
            together, I call complex; such as beauty, gratitude,
            a man, an army, the universe.         --Locke.
      [1913 Webster]

   2. Involving many parts; complicated; intricate.
      [1913 Webster]

            When the actual motions of the heavens are
            calculated in the best possible way, the process is
            difficult and complex.                --Whewell.
      [1913 Webster]

   Complex fraction. See Fraction.

   Complex number (Math.), in the theory of numbers, an
      expression of the form a + b[root]-1, when a and b are
      ordinary integers.

   Syn: See Intricate.
        [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Complex \Com"plex\, n. [L. complexus]
   Assemblage of related things; collection; complication.
   [1913 Webster]

         This parable of the wedding supper comprehends in it
         the whole complex of all the blessings and privileges
         exhibited by the gospel.                 --South.
   [1913 Webster]

   Complex of lines (Geom.), all the possible straight lines
      in space being considered, the entire system of lines
      which satisfy a single relation constitute a complex; as,
      all the lines which meet a given curve make up a complex.
      The lines which satisfy two relations constitute a
      congruency of lines; as, the entire system of lines, each
      one of which meets two given surfaces, is a congruency.
      [1913 Webster]

WordNet (r) 3.0 (2006):

complex
    adj 1: complicated in structure; consisting of interconnected
           parts; "a complex set of variations based on a simple
           folk melody"; "a complex mass of diverse laws and
           customs" [ant: simple]
    n 1: a conceptual whole made up of complicated and related
         parts; "the complex of shopping malls, houses, and roads
         created a new town" [syn: complex, composite]
    2: a compound described in terms of the central atom to which
       other atoms are bound or coordinated [syn: complex,
       coordination compound]
    3: (psychoanalysis) a combination of emotions and impulses that
       have been rejected from awareness but still influence a
       person's behavior
    4: a whole structure (as a building) made up of interconnected
       or related structures [syn: building complex, complex]

Moby Thesaurus II by Grady Ward, 1.0:

211 Moby Thesaurus words for "complex":
   Byzantine, Chinese puzzle, Diana complex, Electra complex,
   Gordian knot, Herculean, Oedipus complex,
   Rube Goldberg contraption, abstruse, acculturation, amalgamated,
   ambiguous, ambivalent, amphibious, arduous, baffling, balled up,
   bewildering, beyond one, blended, brutal, can of worms,
   castration complex, civilization, collectivity, combined,
   complicated, composite, compound, compounded, compulsion,
   confounded, confounding, confused, confusing, conglomerate,
   convoluted, crabbed, cramp, critical, cultural drift, culture,
   culture area, culture center, culture complex, culture conflict,
   culture contact, culture pattern, culture trait, daedal, dappled,
   delicate, demanding, devious, difficile, difficult, distracting,
   disturbing, eclectic, elaborate, embodiment, embrangled, entangled,
   entirety, equivocal, ethos, exacting, fascination, father complex,
   fifty-fifty, fixation, fixed idea, folkways, formidable, fouled up,
   garbled, gordian, hairy, half-and-half, hang-up, hard,
   hard to understand, hard-earned, hard-fought, heterogeneous,
   hypercathexis, idee fixe, implicated, indiscriminate,
   inferiority complex, integer, integration, integrity, intricate,
   involute, involuted, involved, ironic, irresistible impulse,
   jawbreaking, jumbled, jungle, key trait, knot, knotted, knotty,
   laborious, labyrinth, labyrinthian, labyrinthine, loused up,
   many-faceted, many-sided, matted, maze, mazy, mean, meander,
   meandering, medley, mesh, mess, messed up, mingled, miscellaneous,
   mixed, mixed up, mixed-up, monomania, morbid drive, mores,
   mother complex, motley, mucked up, multifaceted, multifarious,
   multinational, multiracial, mysterious, mystifying, no picnic,
   not easy, obfuscated, obscure, obscured, obsession,
   obsessive compulsion, oneness, operose, organic unity,
   overtechnical, parent complex, patchy, perplex, perplexed,
   perplexing, persecution complex, pluralistic, possession,
   preoccupation, prepossession, promiscuous, puzzling, ramified,
   ravel, reticular, rigorous, rough, roundabout, rugged,
   ruling passion, scrambled, screwed up, set with thorns, severe,
   snafu, snake pit, snarl, snarled, society, sophisticated, spiny,
   steep, strenuous, subtle, superiority complex, syncretic, tangle,
   tangled, tangled skein, tangly, thorny, thrown together, tic,
   ticklish, toilsome, totality, tough, trait, trait-complex, tricky,
   twisted, unity, uphill, vague, varied, webwork,
   wheels within wheels, whole, wicked, wilderness