What magazine (such as The Economist,The TIME) is the suitable for ESL learners to mimic its writing style?
I have never thought of this. As I recall, The New Yorker magazine is said to have one of the most intellectually advanced vocabularies. However, many of the author's they publish are also people with radical and unscientific or illogical ideas. So for my self, I would look toward the author of a non-fiction book.
I will say something on the issue of copying a style, or reading a certain author to learn.
I think personally that Fiction is one of the worst materials to use for study.
If one chooses to prepare for English Language Tests, or want to prepare for using English in a career, all Non-Fiction publications would be so much better.
I think Non-Fiction books would be a better source than a New Magazine like Time. But News Magazines, owing to their diverse "sections" like People, Celebrities, World Affairs, Science, Arts, Politics, could be the source for a Modern Vocabulary and a diverse vocabulary.
I think that an easier method of study, which would tend to have a less complicated vocabulary would involve the readings in human history. Some of the odd adjectives are missing in histories.
Historical accounts are easier to read.
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and so forth