ANSWERS: 2
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You're right, you would look exactly the same as if you were stationary, because if you are holding the mirror it is travelling at precisely the same speed you are, and behaves the same way as it would if you and the mirror were both immobile or travelling at "normal" speeds. See the answer for the question about "headlights on a train travelling at light speed", at the top of this page.
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Sorry, traveling at the speed of light won't improve your looks :)
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