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.

the figures below are made out of circles, semicircles, quarter … find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations). remember that we'll also have to cut whatever areas we get in half, since we're only dealing im pretty sure that is the right answer

step-by-step explanation:

f(x) is going down by 4

step-by-step explanation:

(its either that or its going left by 4)