Question

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?

Answer 1

Answer:

East = 1

South = - i

West = -1

Step-by-step explanation:

We are given that, the robot can only go north, south, east and west.

Assuming that the north-south axis corresponds to the y-axis and west-east axis corresponds to x-axis.

Now, it is provided that the ' i ' represent that robot is facing north.

So, if the robot turns and faces south, it can be seen that he will be facing in the opposite direction of ' i '.

Since, the values on y-axis are negative in that direction.

Hence, South will be represented by ' - i ' .

Moreover, it is given that we use only the numbers whose magnitude is 1. As, west-east axis represents x-axis.

So, the value that represents East will be 1 ( as it is on the positive x-axis ).

Since, west is in the opposite direction of east.

So, West will be represented by -1.