Does in that make my sentence formal? If so, how can I change it to be more neutral?
closed as primarily opinion-based by Jason Bassford, TrevorD, Skooba, choster, J. Taylor Mar 10 at 1:58
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I believe a re-arranged version is more neutral:
They complement one another to form the whole, like pieces of a puzzle.
(One could use '...like the pieces of a puzzle.' here; I see little difference between them.)
There's a great many valid ways this could be re-arranged, but I think this version is the least-belaboured.
You'd really need to specify your target audience if you want to fine-tune a sentence like that. There would be no problem with it in The Atlantic, say, or The Economist, but it might stand out in People as the phrase in that is not in the working vocabulary of a good percentage of native speakers.
If you wanted to get rid of it entirely and were willing to reorder your sentence
Like the pieces of a puzzle they complement one another.
But even the word complement would give some readers trouble.
If you want also to say "to form the whole" you're back to square one again, as the register of that phrase, with "the whole", is elevated above conversational— again for a large percentage of native speakers but by no means all.
P.S. If you find yourself explaining your metaphor, you're generally on thin ice.