Mbedtls_rsa_complete does not build RSA private key from modulus and private exponent only

Hello and thank you for considering this!

Is there a specific reason why mbedtls_rsa_complete requires more than the modulus and the private exponent for building a RSA private key?
Having the RSA key pair (public and private) in the form of modulus and public/private exponents should be enough to build both keys.
The public key is alright, the private key isn’t.

Thank you!