Dear Angélique,
If I understand correctly, you'd like the branching logic to be 1) when "Follow-up log" is marked "Completed" AND 2) [follow-up_j1_arm_1][symptom]=VALID?
You have here 2 options:
1) The branching logic corresponding to "EMPTY" is written like this:
[suivi_j1_arm_1][symptome]= ""
2) You could also write it as "NOT EQUAL TO ALL RESPONSES" (wich is written with <> symbol in REDCap):
[suivi_j1_arm_1][symptome]<> "REPONSE1" OR [suivi_j1_arm_1][symptome]<> "REPONSE2" ...
By the way, since you wrote "[...] as well as to participants who answered '0'" I think you should replace your AND with an OR:
And in this case, then you must use option 2), otherwise the invitation will be sent to any new record, since the field is necessarily empty as soon as someone opens the survey.
Best,
C.