This part of the sentence is correct and usable in written English. You can use it when you want to indicate that two or more things are compatible and/or reinforce each other. For example, "The members of the team have different skills and areas of knowledge, but they are complementary to each other and work well together.".
But our jobs are complementary to each other rather than competitive.
The overhangs are complementary to each other.
These are complementary to each other.
Genetic and agronomic biofortification are complementary to each other.
Consequently, motors and brakes are complementary to each other.
Both models are complementary to each other at this junction.
"We believe that medicine and basic research are complementary to each other.
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Cristina Valenza
Retail Lead Linguist @ Apple Inc.