In your sentence, "complexity" is a noun and the object of the preposition "of". We can ignore the words "high" and "project" because they are just adjectives modifying the noun, so they change nothing. You can say "complexity", "a complexity", or "the complexity". All are correct. Use "a" to refer to a non-specific complexity. Use "the" to refer to a specific complexity. Use neither to refer to the general category of all that is complex. "Danger" would work the same way. You could be mindful of danger, meaning anything and everything that might be dangerous. Or, you could be mindful of one specific or non-specific danger.

Complexity is usually a non-countable noun. Therefore, we don't usually use indefinite articles with this word. I hope this answers your question.