Why is "mir" used in these sentences?
- "Ich bin mir sicher." - "I am positive."
- "Ich kann mir vorstellen ..." - "I can imagine ..."
It doesn't appear in the translation. Also "Ich" looks sufficient.
Both are reflexive verbs that can also be used in a non-reflexive way.
Reflexive verbs are more common in German than in English (like "enjoy yourself").
"Ich bin mir sicher" works with or without the "mir", but "Ich kann mir vorstellen" does not, because the reflexive version "sich (etwas) vorstellen" (=> imagine something) has a different meaning than the non-reflexive version "(jemanden) vorstellen" (=> introduce someone).
Here, you can find more about this subject.