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The phrase "are complex and required" is correct and usable in written English.
It can be used to describe something that is both intricate and necessary in a particular context.
Example: "The procedures for this project are complex and required to ensure safety and compliance."
Alternatives: "are intricate and necessary" or "are complicated and essential."
Exact(1)
However, the relationships between anisotropy and fractures are complex and required further technical development.
Similar(59)
They are complex and require specialist knowledge.
Some actions are simple and can be taken by individual companies, others are complex and require collaboration.
Both phases are complex and require exquisite organization of multiple cellular systems, including interactions between proteins and cellular membranes.
They are complex and require explicit directives and assessments of an instructor.
Modern interconnected electrical power systems are complex and require perfect planning, design and operation.
However, such methods are complex and require analysts to make many assumptions and approximations.
Such problems are complex and require a rigorous and systematic approach to identify the best solution.
Coverage decisions are complex and require the consideration of many factors.
Cardiac surgical procedures are complex and require the coordinated action of many.
"The issues presented in this matter are complex and require a complex understanding of the market system".
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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