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Forget - 忘 vs 忘记

Generally speaking ,“忘"can't be used alone , it often be used with other Chinese characters，such as "忘记"，"忘了" ,"忘不了"and so on .

“忘”is almost the same with "忘记".
"忘" is mostly used in spoken Chinese. "忘记"can also be used in spoken Chinese, but a little bit more formal.
忘----verb. 我忘了。 我没忘。
忘记----verb 我忘记了。 我没忘记。

in gerenal,他们是相同的，“忘”很多时候用于口语上，“忘记”更书面一些 more formal

Same:
Both 忘 and 忘记 can mean forget something(somebody) or forget to do something.

Different:
1. 忘记 stresses that something slip from your memory.
2. 忘了 can put at the end of a sentence but 忘记 could not. There must be something follow after 忘记.
ie: Don't forget it！ 别忘了！
I'm sorry, I forgot. 对不起，我忘了。
3. The usages of the two words are different.

Forget to do something.
ie: I forgot to do my homework.
我忘记写作业了。
我忘了写作业。
ie: I forgot my passport.
我忘了带护照。
我忘记带护照了。

Forget something or someone.
ie: I won't forget her.
我不会忘记她。
我不会忘了她。
ie: I didn't forget you.
我没有忘记你们。
我没有忘了你们。

Ask someone don't forget something. （usually don't use 忘记）
ie: Don't forget your bag.
别忘了你的书包。

忘了，langue orale
忘记，langue écrit ,peut aussi être utilisé dans la langue orale.

Je voudrais étudier la France .nous nous aidons réciproquement. Je parle la France en peu .je peux dire la culture chinoise.je trouve que vous aidez à apprendre le chinois.

是相同的

忘 is short of 忘记