Two coins are tossed. if a is the event "two heads" and b is the event "two tails", are a and b mutually exclusive? are they complements?

For the first one, yes they are mutually exclusive because:
- If event A happens it is impossible for event B to occur 

- If event B happens it is impossible for event A to occur 

For the second question, they are not complements.

To be complements the sum of the probabilities of the two events MUST add to 100%. In this situation, if you toss two coins, you can also get ONE head and ONE tail. In short, they are not complements because Event A + Event B do NOT equal 100% of all possible outcomes when tossing two coins.