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"complementary purposes" is correct and usable in written English.
You can use it when you are describing two different things, concepts, etc. that work together to achieve a goal. For example, "The two different departments had complementary purposes, which allowed them to come together to create a successful outcome."
Exact(10)
Because fines and damages serve different but complementary purposes, it is generally the rule that civil fines collected by government are retained by government, not returned to the victims.
The pledge distributed here reads, "I pledge to investigate thoroughly and weigh the social and environmental consequences of any professional activity that I may undertake". The pledge has two complementary purposes.
The scheme described here would, in contrast, deliver the two tunable monochromatic undulator beams to separate endstations that address rather different and somewhat complementary purposes, with further beam conditioning imposed as required.
From the outset, phase-encoded designs were used for two related, but complementary purposes: 1) to measure aggregate response properties of neurons in a voxel, for example the average visual field location of receptive fields, and 2) to segregate the set of voxels that corresponds to an organized cortical region, for example a retinotopically mapped visual area.
This man likely has timepieces worth more than many houses and this iPad will be used for the same complementary purposes as yellow gold simply doesn't go with everything.
Our findings suggest that inter-organisational links served two important and complementary purposes: material and symbolic.
Similar(50)
1.This volume thus has a very different, although complementary purpose to the earlier volume Laboratory experimentation in economics: Six points of view (Alvin E. Roth, editor, Cambridge University Press, 1987).
Given that § 6.5.1 clearly covers the affirmative obligations of the parties in the regulatory context, it disrupts the sensible structure of the Merger Agreement to read § 6.5.6 as being other than what it purports to be: a negative covenant that has the limited and complementary purpose of prohibiting parties from taking affirmative action with the likely effect of impeding the Merger's closing.
But Post-Its serve a similar complementary purpose as Evernote itself--taking notes.
Amino-acid tracers, such as MET, perform better for this purpose and thus play a complementary role to FDG.
The expert panel also identified four areas of research priority: 1) Prevalence of complementary medicine use; 2) purpose of complementary medicine use (whether for a specific condition, general wellness, or both); 3) disclosure of complementary medicine use to conventional providers; and 4) inventory of natural supplements and prescription medications (not fielded due to logistical reasons).
More suggestions(15)
complementary reasons
complementary pursuits
complementary orders
complementary missions
supplementary purposes
complementary objectives
complementary implementation
reinforcing purposes
complementary aim
supplementation purposes
overlapping purposes
complementary mission
complementary subject
complementary objective
supportive purposes
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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