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Discover LudwigThe phrase "real part" is correct and can be used in written English.
It is typically used to differentiate the "real" or literal meaning of something from an imagined or symbolic one. For example: "The real part of the story is much more serious than the made-up parts."
Dictionary
real part
noun
Of a complex number a + bi, the value a.
Exact(60)
"They are a real part of our culture.
"I can be a real part of the team".
Itchy, fortunately, plays no real part at this point.
Left, real part.
real part imaginary part.
(a) Real part, ϵr.
This is part real, part concept.
where denotes the real part.
where Re means real part.
where denotes the real part of.
where ℜ stands for the real part.
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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