When you start a sentence with acronyms such as i.e., e.g., or similar, how do you capitalize them? "I.e., ...", or " I.E., ..."? Thanks.
At the beginning of a sentence, capitalize the first letter:
E.g., a sentence like this one.
Inside a sentence, both letters go in lower case:
Both letters go in lower case, i.e., neither is capitalized.
Capitalization for Latin abbreviations works the same as if you were to spell out the words (which no one ever does). They're not acronyms. The second letter stands for the second word of the phrase (exempli gratia or id est), so you don't capitalize it, just as you don't normally capitalize the second word of a sentence.
If you did spell out the words, here's how the sentences would look:
Exempli gratia, a sentence like this one.
Both letters go in lower case, id est, neither is capitalized.
The principle is probably clearer if you see it with a Latin abbreviation where a word is abbreviated with more than one letter. Op. cit., which means "in the work (previously) cited" (opere citato), naturally gets only the O capitalized at the start of a sentence, since we normally capitalize only the first letter of the first word of a sentence.
More about "Latin in English" is here, including an explanation of what the abbreviations stand for.
If you find that you have to start your sentence with such an abbreviation, then capitalize the first letter, as Ben explains in his answer.
However, it's usually best to avoid starting a sentence with such an abbreviation. This should not be construed as any sort of a 'rule', simply a stylistic guideline. Regardless of whether you capitalize it correctly or not, it's going to look odd.
As TRomano suggested in comments,
You avoid the problem by using a semicolon (or a comma, if the syntax allows) rather than a full stop after the preceding clause. As a general rule of thumb, don't start sentences with abbreviations for Latin phrases. Most of them don't start a new idea in any case, but are continuations of the prior thought.
StoneyB goes so far as to suggest that
By and large, if you're working in a register where i.e. or e.g. would be appropriate you probably shouldn't be using them at the beginning of a sentence. It's not strictly ungrammatical, but it's distinctly awkward. Moreover, some academic style manuals now explicitly deprecate these Latinisms; use "that is" or "for example" instead.
I've found that a lot of people don't know what these letters stand for, and often mix them up. Using English phrases instead is not bad advice, especially at the start of a sentence.
You capitalize the first initial, e.g.
E.g., I hate rum.
I.e., I hate all rum.
The Chicago Manual of Style says not to italicize common Latin abbreviations (and words).
7.53 Roman for Latin words and abbreviations
Commonly used Latin words and abbreviations should not be italicized.
There is no rational reason not to start a sentence with e.g. or i.e., just as there is no rational reason not to start a sentence with and.
And note, the abbreviations are italicized in the above sentence, along with and, because I am talking about them. I.e., I am not using them in their normal manner.