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The phrase "a complex manner" is correct and usable in written English.
It can be used to describe a way of doing something that involves multiple intricate steps or is not straightforward.
Example: "The scientist explained the phenomenon in a complex manner, making it difficult for the students to grasp the concept."
Alternatives: "a complicated way" or "an intricate fashion".
Exact(60)
The orientation textures of these two lamellar populations depend upon processing conditions in a complex manner.
The opacity, κ, can be calculated for any temperature, density, and chemical composition and is found to depend in a complex manner largely on the two former quantities.
The remainder, most notably Aquitaine and the area around Bayeux, was divided in a complex manner; and Paris was subject to joint possession.
The evolution towards those {116} facets happens in a complex manner through high-index facets.
TRESK is activated in a complex manner by intracellular calcium signalling.
Recurrent or chronic headache and psychiatric comorbidities interact in a complex manner.
It depends in a complex manner on the initial sorbitol content.
Biochemical reactions from proteolysis and glycogen metabolism interrelate with the sarcomere length in a complex manner.
DoE results revealed that the parameters interact in a complex manner and depends on the responses.
Cutting force during 5-axis end-milling is affected by many factors in a complex manner.
All the six pathways are interrelated and coordinated in a complex manner.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com