Well the question is highly hypothetical. I'll try to make it simple for you to understand. Let the source to be a car's headlights. And the car itself is moving with speed of light(which is practically near to impossible). As mentioned earlier now-Imagine that you are in your car 'traveling at the speed of light' and that you turn on your headlights. That state of motion is utterly equivalent to being at rest in an empty universe. Since, when at rest, the light from your headlights would be launched forward from your car at the speed of light, relative to you, with a certain color spectrum, that is exactly what would happen if somehow you could be moving instead at the speed of light. Hope it answers your question. All the best!