'extreme complexity' is a correct and usable phrase in written English.
You can use it when you are trying to describe a situation or object that is very complex and difficult to understand. For example: "The inner workings of the engine had an extreme complexity that stumped even the most experienced mechanic."
Mathematical and computational models are required to understand the extreme complexity of living systems.
That is a famous fact; it is said to have contributed to the extreme complexity of James's late-period style.
This may give the impression of extreme complexity, whereas for the ear the piece unfolds naturally and homogeneously.
But the extreme complexity and detail needed to represent timing, direction, impulse and dynamics make it the province of very few specialists.
Intensive-care medicine has become the art of managing extreme complexity — and a test of whether such complexity can, in fact, be humanly mastered.
Systems and measures that are put in place need to be able to deal with extreme complexity, especially in relation to outbreaks in fragile States with weak institutions.
However, direct implementation of room responses generally proves impractical due to the extreme complexity of system dynamics.
The extreme complexity of the nervous system does not provide a favorable medium for the development of deterministic connections.
The molecular mechanisms that regulate their transcription, in normal, stress, or pathological conditions, are characterized by extreme complexity and subtlety.
This HW/SW heterogeneity is a source of extreme complexity in the control system regarded as a whole.
Even these do not exhaust the meanings that have been attached to the philosophical enterprise, but they give some idea of its extreme complexity and many-sidedness.
