adj

• (mathematics, of a number) Having the form a + bi, where a and b are real numbers and i is (by definition) the imaginary square root of −1.
  "complex number"
• (mathematics, mathematical analysis, of a function) Whose range is a subset of the complex numbers.
  "complex function"
• (mathematics, algebra) Whose coefficients are complex numbers; defined over the field of complex numbers.
  "complex polynomial"
• (geometry) A curve, polygon or other figure that crosses or intersects itself.

noun

• An assemblage of related things; a collection.
  "Since then, a good deal of research has documented and concluded that the nominal species A. fraterculus actually comprises an unresolved complex of cryptic species."
• (psychology) A group of emotionally charged ideas or mental factors, unconsciously associated by the individual with a particular subject, arising from repressed instincts, fears, or desires and often resulting in mental abnormality.
  "Jim has a real complex about working for a woman boss."
• (psychology) A group of emotionally charged ideas or mental factors, unconsciously associated by the individual with a particular subject, arising from repressed instincts, fears, or desires and often resulting in mental abnormality.
• (chemistry) A structure consisting of a central atom or molecule weakly connected to surrounding atoms or molecules, as for example coordination complexes in inorganic chemistry and protein complexes in biochemistry.
  "Oxygen levels on Earth skyrocketed 2.4 billion years ago, when cyanobacteria evolved photosynthesis:[…]. The evolutionary precursor of photosynthesis is still under debate, and a new study sheds light. The critical component of the photosynthetic system is the “water-oxidizing complex”, made up of manganese atoms and a calcium atom."

verb

• (chemistry, intransitive) To form a complex with another substance.
• (transitive) To complicate.