As a recent grad, here's my opinion (for what it's worth): nobody cares about an identity. In fact, all of the interviews and informational meetings I've gone to have cared more about my personality and my work than any kind of overt "personal identity" in the form of a logo.  Why do you even need your own logo in the first place? The sentiment I've gotten from people is that the idea of a "personal identity" is overwroght and—quite frankly—a bit unnecessary in the long run.

What resonates more with people is a personal story. Who you are, where you're coming from as a designer, what your opinions are about things. Those matter so much more than some overdesigned narcissistic logo. Also: letterhead and envelopes? Really? If you're going to design and produce something that you're actually writing on and mailing, you'd be much better off making a batch of thank you notes for your first interviews (I really mean that: I've sent handwritten thank you notes to each and every person that has taken the time to sit down with me. It's a fantastic way to leave a good impression. You can even have some fun with it: http://bit.ly/HAI4Ay)

Want my opinion? Finish the assignment, but do it in a design that you'll actually use. If you can find a way to ditch the arbitrary "envelope & letterhead", all the better. I'd do business cards and thank you notes. You'll be using both of them a ton soon enough.

No doubt you'll have to suck it up and do the asignment. You'll will, over your (hopefully long and successful) creative career find yourself working on projects you aren't fully invested in as an idea. You'll here professional designers claim they only work on what they want to work on, but out of thousand designers, that's true for about... 5 at most. And they worked hard to earn that right. I'd through a business card (and maybe even a website) in there with the letterhead and envelope like John suggested. I agree with John's point about a personal story being your true selling point. I've been on the hiring end of that equation and the person with talent + personality always gets the job over the slick portfolio + lame attitude candidate. Maybe approach this project (and this may be your teacher's point in assinging it) as a branding exercise. Brand = story + identity. More to the point, your identity should communicate your story. I suggest taking the BRAND approach and see how far you can transalte your story through design. That it will make it more interesting to work on and maybe give you nice "case study" versus "cool design" for you portfolio (always a much better sell). Hope that helps!

I agree with John. Great feedback :)

More than anything I think this is excessive from a sustainability standpoint. It's environmentally wasteful and quite simply irresponsible to ask a class to print out 100 copies each of something that will potentially be wasted (for reasons listed above: evolving identity, lack of need), and depending on the number of students in the class, this can REALLY add up...  These days we are able to share our identities digitally, and it's unlikely that a physical copy will be necessary 100 times before you're ready to once again evolve your visual sense of self.