1. Which one is correct to say-
a. He resigned from his job.
b. He resigned.
They are both correct as long as the context is clear. (b) is more likely than (a) when the speaker is a colleague.
Another question is
2. Which one is polite way to ask teacher
a. I won't be able to attend the class next week because we are moving to another apartment.
b. I can not attend the class next week because we are moving to another apartment.
They are both fine as far as I am concerned. There is a difference though - (a) is more formal than (b). Also, it would be better to say 'can't' instead of 'can not' in (b).
Student or Learner