Relative motion of C on C formula

I need to prove the affect of relative motion on C if the velocity is C. The Relativistic Doppler Affect is not accurate correct? I am calculating only direct motion no adjustments for radial velocity etc. needed

 

I do not know if this will work, I will look into it, thank you. Hyperphysics seems to be pretty trusty right? Not to ask another question before I try your solution but just to firm things up, I am looking into a hypothetical question(which I know do not always have answers :) ). The question posed basically involves a vehicle traveling at C and then emitting light. I am in search of the most accurate formula for calculating the shifts in wave length. I had a quick chat with an unknown physics professor who passed the dry erase board I was using. He had enough time to tell me, I think, that Relativistic Doppler Shift Formula is not the most accurate for this, but not much else. Though with the R.D.S.F I think I can still "legally" get the answer of 1.0. This would be a one hundred percent increase in wavelength which, to me, makes sense. Though I have muddied my own waters and catch myself mixing in things dealing with absorption lines. haha :) any help would be much appreciated and thanks for the post!

 

The question is I posed for my essay to help show the parameters of relativity. By accurate I did not mean it was flawed and I don't appreciate the slight sense of sarcasm that seems to accompany most answers on this site. By accurate I simply meant could think of a form of an equation that gives concrete meaning, or is correct or by definition equivalent. The main reason of this post was poorly asked. So my bad. The part I am struggling with is that when looking at formulas and thinking of physical circumstance, which are obviously interchangeable I can't think of a reason why you can't, simply speaking of light as it relates to doppler shift, figure out the frequency of c when the source of c's relative velocity is c. I have yet to prove why or why not this means breaking the speed of light. In my mind it does not. The relativistic form you gave just simply shows that the SPEED of light for c when it's source is c equals c. When I think of this question it seems the redshift for this type of question should be one hundred percent but can not prove or disprove this, someone help.

 

from the point of reference of inside the car