For a Precalculus assignment, I am supposed to write two expressions that describe what happens when you rotate a robot 90 degrees left or right on a complex coordinate plane. The magnitude equals one. If the robot is facing south, the direction, d, is -i. If the robot is facing north, d = i. If the robot is facing east, d = 1. If the robot is facing west, d = -1. This is what I have come up with so far: Table of Values
For left turns, I have been thinking about the ways to turn -1 into -i, 1 into i, i into -1 and -i into 1. I know that the square root of negative one is i and that i^2 is -1. I can use this knowledge to turn left for each of the above values, but I can't think of a single expression to write for d that would give me d - 90 degrees for each situation. For example, to turn left from -1 to -i, I could take the negative square root of -1 to equal -i, but to turn i into -1, I have to square i. I don't want anyone to do my homework for me, but could anyone give me a hint to write these expressions? Am I on the right track, or should I think about the problem differently?
Thanks
PS: I'm still learning how to use this site. If I'm not supposed to ask homework questions on here, let me know and I will stop.