The Collaborative International Dictionary of English v.0.48:

Complexity \Com*plex"i*ty\, n.; pl. Complexities. [Cf. F.
   complexit['e].]
   1. The state of being complex; intricacy; entanglement.
      [1913 Webster]

            The objects of society are of the greatest possible
            complexity.                           --Burke.
      [1913 Webster]

   2. That which is complex; intricacy; complication.
      [1913 Webster]

            Many-corridored complexities
            Of Arthur's palace.                   --Tennyson.
      [1913 Webster]

WordNet (r) 3.0 (2006):

complexity
    n 1: the quality of being intricate and compounded; "he enjoyed
         the complexity of modern computers" [syn: complexity,
         complexness] [ant: simpleness, simplicity]

Moby Thesaurus II by Grady Ward, 1.0:

31 Moby Thesaurus words for "complexity":
   abstruseness, arduousness, bothersomeness, burdensomeness,
   complication, convolution, crabbedness, crampedness, deepness,
   difficultness, difficulty, esoterica, hairiness, hardness,
   inscrutability, intricacy, involvement, knottiness, laboriousness,
   onerousness, oppressiveness, profoundness, profundity,
   reconditeness, rigor, rigorousness, ruggedness, strenuousness,
   toilsomeness, toughness, troublesomeness



The Free On-line Dictionary of Computing (30 December 2018):

complexity

    The level in difficulty in solving mathematically
   posed problems as measured by the time, number of steps or
   arithmetic operations, or memory space required (called time
   complexity, computational complexity, and space complexity,
   respectively).

   The interesting aspect is usually how complexity scales with
   the size of the input (the "scalability"), where the size of
   the input is described by some number N.  Thus an algorithm
   may have computational complexity O(N^2) (of the order of the
   square of the size of the input), in which case if the input
   doubles in size, the computation will take four times as many
   steps.  The ideal is a constant time algorithm (O(1)) or
   failing that, O(N).

   See also NP-complete.

   (1994-10-20)