If you translate 'and suddenly, I'd realised that I could not live without you' as 'et soudain, je m'étais rendu compte que je ne pouvais pas vivre sans toi', the past participle is corrected to 'rendue' (because it's a female speaker). But my understand was that 'compte' is the direct object in this phrase and 'me' the indirect, and that therefore the past participle is invariable.
Freeform Writing Exercise C1
The participle in se rendre compte does NOT agree with the sex of the speaker. Just as you suspected, compte is treated as the direct object. See, e.g., here, at the very bottom of the page:
For this reason, it is, eg., Marie s'est rendu compte. (And not rendue.)
Bonjour à tous,
Chris and Tom are both correct. Thank you for pointing this out! It has now been amended accordingly.
Agreement with Pronominal Verbs
Merci et bonne journée !
The above reference tells me that the locution verbale "se rendre compte de (qch)" --> réaliser.
This may help you to understand the grammar to your satisfaction. I'm not sure that "compte" is the direct object -- but simply within the locution verbale above.
I hope that this may help.
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