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" If you are traveling in a car at the speed of light and you turn on your headlamps, will the light emitted illuminate the path in front of you?"

I am not concerned with the car or its occupants in any way. The effect of relative motion at the speed of C on white light is more the point of this essay. In an effort to create a well rounded paper, I am trying to use the Reference frames of; motionless & behind the car, motionless & in front of the car and inside of the car looking forward. I have tried to use the Relativistic Doppler Shift Formula to calculate these. My attempt at calculating the blue shift yielded a value of -1.59578... for Z. I had expected to get an answer of 1 or -1. Which, I think, would mean a relative motion of hundred percent of the speed of light.

"Is it still accurate to use the Relativistic Doppler Shift while using C for the velocity?"