The phrase "a number of complexities" is correct and usable in written English.
It can be used when discussing various intricate issues or challenges related to a particular topic or situation.
Example: "The project faced a number of complexities that required careful planning and coordination among team members."
Alternatives: "several challenges" or "multiple intricacies".
"As the questions on the survey explored deeper and more complex areas, we noted a number of complexities.
There are obviously a number of complexities involved in the application of a new regulation.
They have said that this is a unique school, with 74 different languages spoken and a number of complexities.
The seemingly straightforward task of analysing faecal egg counts resulting from laboratory procedures such as the McMaster technique has, in reality, a number of complexities.
After doing that, it is clear that Boulevard du Temple possesses a number of complexities or ambiguities which have received little accounting from me, and perhaps from others, so far.
In view of service-oriented architecture (SOA) and Web services, there have been numerous extensions and enhancements to these traditional technologies, including XML Parsers and similar capabilities, and there also continue to be a number of complexities.
In the paper Areces, Blackburn, and Marx (1999), a number of complexity results are given for hybrid modal and tense logics over various classes of frames, for example arbitrary, transitive, linear, and branching.
In Section 'What does a good IDS signature look like?' we identified a number of complexity features for the triggered signatures and highlighted that good signatures will tend to exhibit much higher values compared to the regular ones.
There are a number of methodologic complexities associated with research regarding depression and cardiovascular disease, including difficulties in the definition and measurement of depression, complexities in the conduction of large-scale trials, ethical considerations surrounding the use of placebo, and interpretation of trial results.
There are a number of other complexities that arise during the process of functional verification.
This paper explores a number of underappreciated "complexities" in the interpretation of the taxonomic composition, sex ratios, and mortality profiles of archaeological faunal assemblages.
