What is the maximun number of trails Charlie could fit in a single picture?

When navigating the maze, the robot will only need to go north, south, east, and west. it can be useful to use the complex plane to represent these directions. when using the complex plane this way, we use numbers such that their magnitude is equal to 1. if we let the value i represent the robot facing due north, what values represent the robot facing east, south, and west? n=i s = -i e =1 w = -1 the arrow at the maze entrance indicates that the robot will be heading east when it enters the maze. when programming the robot, let the complex number d represent the direction the robot is facing. as the robot changes direction, the value of d will also change; so, the value of d is dependent on where the robot is in the maze. at the start of the maze, what is the value of d? d=1 while navigating the maze, the robot will need to be able to turn left and right. the first turn the robot will make is a left turn. what will the value of d be after the first turn?