A partial solution!
In a personal communication to me, Ron Lipman of Louisville correctly named Lewis Carroll as the author of the mystery poem containing an allusion to the complex number
(-7/2) + (i(sqrt(445/3))/2)
Mr. Lipman put the available clues together -- a British author who flourished between 1850 and 1900, who wrote poetry, and who (from the nature of the puzzle) must have had some interest in mathematics -- to arrive at the author's identity.
THE CONTEST REMAINS OPEN, however, since no one has yet identified the poem or derived the number from its text.
Here are the clues that remain relevant in the light of Carroll's identification:
(1) The poem appears in the standard editions of Carroll's complete works. (Note that editions of Carroll's complete works exclude the strictly mathematical works that he wrote under his real name, Charles Lutwidge Dodgson.)
(2) The poem is untitled (and, so far as is known, was never titled).
(3) The poem was written between 1850 and 1898 (the date of Carroll's death; his literary career began in 1845).
(4) The principal subject of the poem is not mathematics.
I will add another clue:
(5) The only mathematics needed to extract the number from the text is that taught in first-year algebra.
As before, to win the $20 Destinations Booksellers gift card, a solver must give the first line of the correct Carroll poem and explain how the number is derived from the text of the poem.
Again, the derivation is fair. No tricks are involved -- you don't have to count letters or know how long Alice Liddell's hair was, or anything at all beyond the actual text of the poem and first-year algebra.
However, I will now accept solutions e-mailed to me at asilofreak[n-o-s-p-a-m]@yahoo.com (delete the brackets and everything between them) or posted as a comment to this post.

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