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The phrase "in a complementary way" is correct and usable in written English
You can use it to describe two things that go together well or mutually support one another. For example: "The two solutions work together in a complementary way to solve the problem."
Exact(60)
Both the positron lifetime and coincidence Doppler broadening techniques were used in a complementary way.
Our results indicate that this relationship can also be viewed in a complementary way.
In this paper these two techniques are used together in a complementary way.
The study is unique as it integrates the Servqual scale and the Kano model in a complementary way.
This study is innovative as it combines several tools in a complementary way to enable data based decision making.
Rugby has to evolve in a complementary way rather than explosions taking place in one part of the game or structure.
We then show how to couple the location estimation and shape reconstruction in a complementary way to improve accuracy for range estimation.
Then, it was determined that the film formed with IHF presents some distinctive component characteristics which interact in a complementary way improving film passivity.
However, a systematic approach, where these technologies are used in a complementary way to supply the shortfall in food and address nutritional deficiencies has not been attempted.
While the two dimensions are substitutes in the abstract computerized environment, they work in a complementary way to increase public goods contributions in the virtual world environment.
We discuss the advantages of the methods used and the benefits of using them in a complementary way for the design of new trawl gears.
More suggestions(16)
in a further way
in a complimentary way
in a supportive way
in a supplementary way
in a complementary direction
in a complementary style
in a complementary mode
in a complementary method
in a compatible way
in a complementary fashion
in a complementary manner
in a timely way
in a cute way
in a funny way
in a complementary laboratory
in a poor way
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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