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"are complementary with" is correct and usable in written English.
You can use it when you want to describe two things that complement each other, i.e., create a complete result when combined. For example: "Their strengths and weaknesses are complementary with one another."
Exact(38)
An assortment of Greek dessert pastries are complementary with dinner.
Salads are complementary with entrees, but there are two $5 versions that are worth the splurge.
Primers R1 and F3 contained 25-nt sequences that are complementary with the antibiotic selection cassette at their 5' ends.
So maybe office workers will soon be wondering whether their skills are complementary with the computer's, or whether it would actually do better on its own.
Such methods are complementary with traditional geometrically-based cross-section analysis tools, as they enable mechanical validation of geometric interpretations.
The schedules for the one-year and two-year tracks are complementary with no overlap between clinical duties of the two fellows to ensure individually enriching experiences.
Similar(22)
"Teaching is complementary with research," says economics professor Alberto Abadie.
As she explains it, her pleasure principle has always been complementary with her business sense.
For this purpose, the approach is adapted to be complementary with practical in parts adjoint sensitivities.
I always want a menu with complete balance, a menu where you can taste every element and every element is complementary with every other one.
They said the project was complementary with their plan and that they were trying to start an industry discussion of the issue.
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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