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'more complex way' is correct and usable in written English.
You can use it when referring to a situation or problem that has more than one solution or that may require more than one approach. For example: "We must find a more complex way of solving this problem, as the current solutions have not been successful".
Exact(59)
This could actually be used in a more complex way.
"They're coming at these issues in a much more complex way".
It was Jane Jacobs who taught us again to view the city in a deeper, more complex way.
His first lesson on the job is that women frequently derive sensual happiness in a more complex way than men.
I thought that the media coverage sensationalised these cases, and this drove me to try to communicate the questions they raised in a more complex way".
I do, however, understand those who felt that it lacked depth, and would add that The Americans covers similar ground in a more complex way.
Battery Park City seems to have been built against a catastrophe; but also, in a more complex way, against the severe beauty of the city.
The flip-side of America's economic dynamism is that it has become more unequal but in a more complex way than first appears (see article).
The crust within the continents, unlike the oceanic crust, is considerably older and thicker and appears to have been formed in a much more complex way.
It makes you explore your whole repertoire as well as make you explore the workings of the world in a deeper and more complex way than most roles do.
A more complex way is to invest a proportion of the capital in something safe, such as zero-coupon Treasury bonds, so that at the target date it yields most or all of the principal sum.
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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