PRECALC HELP PLEASE WILL GIVE BRAINLIEST

  d ⇒ di^(21-22) = -di, facing right from where it was; order doesn't matter

Step-by-step explanation:

For direction defined as 1, i, -1, -i, a left turn is accomplished by multiplying by i. Then "L" left turns will be multiplication by i^L.

A right turn is equivalent to multiplication by -i, so R right turns will be multiplication by (-i)^R.

We know that turning left and turning right are inverse operations of each other, so we can also write a right turn as multiplication by i^(-1). Then R right turns will be equivalent to multiplication by i^(-R).

We know from the commutative and associative laws of multiplication that the order does not matter. So, L left turns and R right turns will be equivalent to multiplication by ...

  (i^L)(i^-R) = i^(L -R)

Hence 21 left turns and 22 right turns is equivalent to a turn of ...

  i^(21-22) = i^-1 . . . . one right turn

From an initial facing direction of 'd', the final facing direction after these 43 turns is -di.