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The phrase "are completely convinced" is correct and usable in written English.
You can use it when expressing a strong belief or certainty about something.
Example: "After reviewing all the evidence, we are completely convinced that our approach is the best solution."
Alternatives: "are fully convinced" or "are entirely certain".
Exact(7)
3. Convince your opponent that you are emotionally dedicated to your position and are completely convinced that it is reasonable.
"We are completely convinced of the intent to destroy the Ixil ethnic group," Judge Barrios said as she read the hourlong summary of the ruling by the three-judge panel.
The new transport secretary has spoken up for "greater devolution to the nations and regions of the UK" in the past, but it's easy to find luminaries of the London transport firmament who are completely convinced that he doesn't really want to hand down power over Southern.
With that said, we live in a time in which the vast majority of folks on the road are completely convinced they're the world's finest driver.
That's why, despite its marvelous complexity, biologists are completely convinced that life today is the result of this long, slow evolutionary process of genetically based divergence from common ancestry.
"We are completely convinced of the reality of electrons when we set out to build and often enough succeed in building new kinds of device that use various well-understood causal properties of electrons to interfere in other more hypothetical parts of nature" (p. 265).
Similar(53)
It is not surprising that he is one of the few male English writers of his generation whose women characters are completely convincing.
Not everyone is completely convinced.
'I am completely convinced that is what he was doing.
This has been Obama's argument as well, but I have never been completely convinced.
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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