途方も無い

Different declension of the adjective in both plain form and keigo (polite)

Adjective declensions

1. Present tense (used to describe a current state or condition) - 現在形（げんざいけい）-
2. Present negative tense (used to describe a current state or condition, but with a negative meaning) - 現在否定形（げんざいひていけい）
3. Past tense (used to describe a past state or condition) - 過去形（かこけい）
4. Past negative tense (used to describe a past state or condition, but with a negative meaning) - 過去否定形（かこひていけい）
5. Te form (used for connecting adjectives or for making requests) - て形（てけい）
6. Adverbial form (used to modify verbs or adjectives, or to describe the way in which something is done) - 副詞化（ふくしか）

Plain form vs keigo

Plain form is the basic form of a verb or adjective in Japanese. It's called "plain" because it's the simplest and most straightforward form, without any added politeness or formality. Plain form is used in informal situations, such as talking to friends, family, or people of lower status.

Keigo, on the other hand, is a set of honorific language expressions used to show respect, politeness, and formality in Japanese.

In general, plain form is used in informal situations and keigo is used in formal situations. However, it's important to note that there are different levels of keigo depending on the level of formality and the relationship between the speaker and listener. For example, the keigo used with a superior in a workplace setting might be different from the keigo used with a customer or client.

It's also worth noting that keigo can be difficult to master, even for native Japanese speakers. There are many different honorific expressions and rules for using them correctly, so it's important to study and practice them carefully in order to use them effectively.

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