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The phrase "the growing complexity" is correct and can be used in written English.
You can use this phrase when referring to a situation that has grown increasingly complex or complicated over time. For example: "We have had to adjust our strategy to account for the growing complexity of the marketplace."
Exact(60)
The most basic is the growing complexity of businesses.
His last article, in June, was about the growing complexity of shareholder reports.
Critics have had a field day complaining about the growing complexity of Apple software.
But despite the growing complexity of vehicles, there are currently 28, the agency says.
One big source of work is the growing complexity of business regulation.
The development of guilds and confraternities reflected the growing complexity of economic organization.
(In a brief aside, Meacham attributes the Panic of 1837 to the growing complexity of the economy).
In May 2004, Sprint answered the growing complexity of cellphone plans with a much more straightforward approach.
The growing complexity of Africa's challenges can hardly be addressed through reliance on the heroic expeditions of foreign volunteers.
As literature sought to reckon with the growing complexity of human affairs, writers relied on this figure more and more.
The costs of government in Java were rising as a result of the growing complexity of administration.
More suggestions(16)
the growing scope
the mounting complexity
the growing simplification
the growing variety
the growing complication
the growing complex
the growing depth
the growing sensitivity
the growing diversity
the growing magnitude
the growing size
the growing intricacy
the increase complexity
the ever expanding complexity
the production complexity
the progressing complexity
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com