"Are you sleeping?"
My wrong answer: ты спите?
Correct solutions: • Вы спите? • Ты спишь?
Why does the form of "спите" change with the formal vs informal pronoun?
Well, because it does. The Russian grammar requires it. What explanation did expect to hear when asking that question?
I can't tell you much about the etymology, because different verb forms for вы and ты is likely to be a very old common Indo-European feature, and its origin is lost in the ages.
I works like this in most languages (e.g. compare Portuguese «tu dormes?» and «você dorme?», German »schläfst du?« and »schlafen Sie?«).
In Russian, вы is grammatically plural. When you address someone politely, you use plural form as if you were talking to several people. And вы requires a different verb form.
Explaining that it's plural helps. :) Thank you. I guess what I was trying to ask (in a totally fried, tired sort of way) is if it does have a different form and how to understand and remember that fact.
Also, every verb have 6 conjugations. The normal form "to sleep" is спать, the conjugations: Я сплю, мы спим, ты спишь, вы спите, он/она спит, они спят. You could split them up to three singular and three plural, I just like to think of it like the chart I learned in class.