Etymology
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Words related to im-

in- (2)
Origin and meaning of in-

element meaning "into, in, on, upon" (also im-, il-, ir- by assimilation of -n- with following consonant), from Latin in- "in," from PIE root *en "in."

In Old French (and hence in Middle English) this often became en-, which in English had a strong tendency to revert to Latin in-, but not always, which accounts for pairs such as enquire/inquire. There was a native form, which in West Saxon usually appeared as on- (as in Old English onliehtan "to enlighten"), and some of those verbs survived into Middle English (such as inwrite "to inscribe"), but all now seem to be extinct.

Not related to in- (1) "not," which also was a common prefix in Latin, causing confusion: to the Romans impressus could mean "pressed" or "unpressed;" inaudire meant "to hear," but inauditus meant "unheard of;" in Late Latin investigabilis could mean "that may be searched into" or "that cannot be searched into." Latin invocatus was "uncalled, uninvited," but invocare was "to call, appeal to."

The trouble has continued in English; the hesitation over what is meant by inflammable being a commonly cited example. Implume (1610s) meant "to feather," but implumed (c. 1600) meant "unfeathered." Impliable can mean "capable of being implied" (1865) or "inflexible" (1734). Impartible in 17c. could mean "incapable of being divided" or "capable of being imparted." Impassionate can be "free from passion" or it can mean "strongly stirred by passion." Inanimate (adj.) is "lifeless," but Donne uses inanimate (v.) to mean "infuse with life or vigor." Irruption is "a breaking in," but irruptible is "unbreakable."

In addition to improve "use to one's profit," Middle English also had a verb improve meaning "to disprove" (15c.). To inculpate is "to accuse," but inculpable means "not culpable, free from blame." Infestive has meant "troublesome, annoying" (1560s, from infest) and "not festive" (1620s). In Middle English inflexible could mean "incapable of being bent" or "capable of being swayed or moved." In 17c., informed could mean "current in information," formed, animated," or "unformed, formless" ("This was an awkward use" [OED]). Inhabited has meant "dwelt in" (1560s) and "uninhabited" (1610s); inhabitable likewise has been used on opposite senses, a confusion that goes back to Late Latin.

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in- (1)
Origin and meaning of in-

word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."

In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.

em- 

word-forming element meaning "put in or into, bring to a certain state," sometimes intensive, from French assimilation of en- "in, into" (see en- (1)) to following labial stop (-b-, -p-, and often -m-), or from the same development in later Latin in- (to im-). "This rule was not fully established in spelling before the 17th c." [OED], but it is likely the pronunciation shift was in Old French and Middle English and spelling was slow to conform. Also a living prefix in English used to form verbs from adjectives and nouns (embitter, embody). In words such as emancipate, emerge, emit, emotion the e- is a reduced form of Latin ex- (see ex-) before -m-.

imbalance (n.)

1895, from im- "not" + balance (n.).

immeasurable (adj.)

late 14c., immesurable, from im- + measurable. It could alternate with immensurable. Related: Immeasurably.

impanel (v.)

"to fit with panels," 1570s; see im- "in" + panel (n.). Related: Impanelled. Also empanel.

impartible (adj.)

late 14c. as "indivisible, incapable of being parted," from Medieval Latin impartibilis; see im- "not, opposite of" + part (v.). From 1630s as "capable of being imparted," from impart (v.) + -ible. Now little used in either sense.

Impuritan (n.)

"one who is not a Puritan," 1610s, a hostile coinage of the Puritans, from im- "not, opposite of" + Puritan, perhaps also with suggestion of impure.