Final answer:
Option B, 'Science owes its systems of plant classification and its double Latin names for plants and animals to Linnaeus, the eighteenth-century Swedish botanist.' is the correctly written complete sentence. It contains a subject, verb, and expresses a complete thought, making it grammatically correct.
Therefore, the option B is correct.
Step-by-step explanation:
The correctly written complete sentence among the provided options is: "Science owes its systems of plant classification and its double Latin names for plants and animals to Linnaeus, the eighteenth-century Swedish botanist." This is because it contains a subject and a verb and expresses a complete thought without any grammatical errors. The other options are incorrect because option A is a sentence fragment and option C contains unnecessary repetitive information that is already explained in the sentence.