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The phrase "are manifold and complex" is correct and usable in written English.
It can be used to describe situations, issues, or phenomena that are diverse and intricate in nature.
Example: "The challenges we face in climate change are manifold and complex, requiring a multifaceted approach to address them effectively."
Alternatives: "are numerous and intricate" or "are varied and complicated."
Exact(7)
While the underlying motives of terrorists are manifold and complex, American foreign policy has often been one of their complaints.
Its functions which support ecosystem services to humans are manifold and complex.
The nature and origin of pore pressures are manifold and complex.
The gender effects are manifold and complex and deserve to be further addressed and analyzed in a different paper.
The issues surround race and casting, for all their modern, social media-enhanced qualities are manifold and complex, and when a director is lambasted for casting an actor in a role outside his own race — as "Aloha" director Cameron Crowe recently was for having Emma Stone play a woman of Asian origin — it has roots in the Sharif debate.
The reasons for this are manifold and complex and include entrenched cultural practices which lead to girls under-performing.
Similar(53)
The challenges in tackling financial exclusion are manifold and driven by a complex set of interactive factors (basic financial literacy, geographical exclusion, relative costs of financial services and products) as well as being linked to a wide range of social issues.
29, 30 The reasons for noncompliance are manifold and include fear of side effects, complex drug regimens incompatible with everyday life, and dementia.
The pleasures are manifold and fascinating.
The issues are manifold, and a bit dizzying.
"The hazards of translation are manifold and dire.
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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