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.
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            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.
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The Collaborative International Dictionary of English v.0.48:

Perplexing \Per*plex"ing\, a.
   Embarrassing; puzzling; troublesome. "Perplexing thoughts."
   --Milton.
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WordNet (r) 3.0 (2006):

perplexing
    adj 1: lacking clarity of meaning; causing confusion or
           perplexity; "sent confusing signals to Iraq"; "perplexing
           to someone who knew nothing about it"; "a puzzling
           statement" [syn: confusing, perplexing, puzzling]

Moby Thesaurus II by Grady Ward, 1.0:

38 Moby Thesaurus words for "perplexing":
   Byzantine, arcane, baffling, bewildering, bothering, complex,
   complicated, confounding, confusing, convoluted, cryptic,
   discomposing, disconcerting, dismaying, distracting, disturbing,
   embarrassing, enigmatic, flabbergasting, impenetrable,
   incomprehensible, intricate, involved, knotty, labyrinthine,
   mysterious, mystifying, paradoxical, perturbing, problematic,
   puzzling, recondite, riddling, sphinxlike, stupefying, twisted,
   unfathomable, upsetting