I’ll definitely call him next week.

  1. I will 
  2. I would 
  3. Both a & b


'Will' is a modal verb used with promises or voluntary actions that take place in the future. 'Will' can also be used to make predictions about the future.

The correct answer is: I will 

    when you're talking about the future, 'will' is very common and simply way of describing what you anticipate. 'I'll definitely call him next week', here I'll is the contracted form of 'I will'. They both mean the same thing. The only difference is that 'I'll' is usually used in a conversation or an informal context.