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The phrase "a complicated manner" is correct and usable in written English.
It can be used to describe a way of doing something that is intricate or difficult to understand.
Example: "She explained the process in a complicated manner, leaving everyone confused about the next steps."
Alternatives: "a complex way" or "an intricate fashion".
Exact(28)
"Actually, the material seems condensed in a complicated manner, to me".
In each case, the crack growth path changes in a complicated manner.
Such a variation has the tendency of tightening and loosening the cables in a complicated manner.
Trees, composed of multi-scale fractal structures, modify the airflow through and around them in a complicated manner.
(3) The injection rate strongly affects the flow behavior of the core material in a complicated manner.
It is shown that material properties and gas velocity affect the uniformity of particle velocity and temperature in a complicated manner.
Similar(32)
The Sino-Indian conflict will define the 21st century in a more complicated manner than the Soviet-American conflict characterised the second half of the 20th.
If the coupling is weak, however, the effects of damping and disorder on the overall decay are comparable in magnitude, and they interact in a more complicated manner.
The work of communicating and conserving artistic images, with the help of technique, produces the material objects metaphorically called "artistic objects" or "works of art": pictures, sculptures and buildings, and, in a more complicated manner, literary and musical writings, and, in our own times, gramophones and records which make it possible to reproduce voices and sounds.
Thus, both FUV and FIR are tightly related to the star formation in galaxies, but in a very complicated manner.
Artificial neural network model works in a very complicated manner like the neurons of the nervous system of human to make a refined optimal decision based on the data or stimuli.
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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