The Collaborative International Dictionary of English v.0.48:

Perplex \Per*plex"\, v. t. [imp. & p. p. Perplexed; p. pr. &
   vb. n. Perplexing.] [L. perplexari. See Perplex, a.]
   1. To involve; to entangle; to make intricate or complicated,
      and difficult to be unraveled or understood; as, to
      perplex one with doubts.
      [1913 Webster]

            No artful wildness to perplex the scene. --Pope.
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            What was thought obscure, perplexed, and too hard
            for our weak parts, will lie open to the
            understanding in a fair view.         --Locke.
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   2. To embarrass; to puzzle; to distract; to bewilder; to
      confuse; to trouble with ambiguity, suspense, or anxiety.
      "Perplexd beyond self-explication." --Shak.
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            We are perplexed, but not in despair. --2 Cor. iv.
                                                  8.
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            We can distinguish no general truths, or at least
            shall be apt to perplex the mind.     --Locke.
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   3. To plague; to vex; to torment. --Glanvill.
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   Syn: To entangle; involve; complicate; embarrass; puzzle;
        bewilder; confuse; distract. See Embarrass.
        [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Perplex \Per*plex"\, a. [L. perplexus entangled, intricate; per
   + plectere, plexum, to plait, braid: cf. F. perplexe. See
   Per-, and Plait.]
   Intricate; difficult. [Obs.] --Glanvill.
   [1913 Webster]

WordNet (r) 3.0 (2006):

perplex
    v 1: be a mystery or bewildering to; "This beats me!"; "Got me--
         I don't know the answer!"; "a vexing problem"; "This
         question really stuck me" [syn: perplex, vex, stick,
         get, puzzle, mystify, baffle, beat, pose,
         bewilder, flummox, stupefy, nonplus, gravel,
         amaze, dumbfound]
    2: make more complicated; "There was a new development that
       complicated the matter" [syn: complicate, perplex] [ant:
       simplify]

Moby Thesaurus II by Grady Ward, 1.0:

181 Moby Thesaurus words for "perplex":
   addle, addle the wits, ail, amaze, appanage, astonish, astound,
   awe, awestrike, babble, baffle, balk, ball up, bamboozle,
   be Greek to, be beyond one, be incredible, be the matter,
   be too deep, be unbelievable, beat, beat one, becloud, bedaze,
   bedazzle, befog, befuddle, beset, bewilder, birthright, blast,
   boggle, bother, bowl down, bowl over, brave, buffalo, bug, cap,
   challenge, checkmate, circumvent, cloud, complicate,
   complicate matters, concern, confound, confront, confuse,
   contravene, counter, counteract, countermand, counterwork, cross,
   dash, daze, dazzle, defeat, defy, destroy, discombobulate,
   discomfit, discommode, discompose, disconcert, discountenance,
   dish, disorganize, disorient, disrupt, distract, distress, disturb,
   dumbfound, dumbfounder, elude, embarrass, embrangle, ensnarl,
   entangle, escape one, fill with doubt, flabbergast, floor, flummox,
   flurry, fluster, flutter, fog, foil, foul up, frustrate, fuddle,
   fuss, get, gibber, harass, implicate, inconvenience, involve, irk,
   keep in suspense, knock the chocks, knot, lagniappe, largess, lick,
   lose one, louse up, maze, mess up, mist, mix up, moider, muck,
   muck up, muddle, mystify, need explanation, nonplus,
   not make sense, not penetrate, overwhelm, palm oil, paralyze,
   pass belief, pass comprehension, perks, perquisite, perturb,
   petrify, plague, pose, pother, pourboire, prerogative, privilege,
   put out, put to it, puzzle, raise hell, ramify, rattle, ravel,
   riddle, ruffle, ruin, sabotage, scotch, screw up, snarl, snarl up,
   speak in tongues, spike, spoil, stagger, startle, stick, stonewall,
   strike dead, strike dumb, strike with wonder, stumble, stump, stun,
   stupefy, stymie, surprise, talk double Dutch, tangle, throw,
   throw into confusion, thwart, tip, torment, trouble, unsettle,
   upset, vex, worry