Is it true that the meaning of 忌々しい is "annoying"?
What is the root word of 忌々しい and its meaning? Is it 忌まう?
Is it true that the meaning of 忌々しい is "annoying"?
What is the root word of 忌々しい and its meaning? Is it 忌まう?
Expanding on user4092's answer, and in the spirit of exploring word formation patterns, it is worth noting that there are various -しい adjectives that derive from the 未然形【みぜんけい】 (incomplete form) of verbs. Examples:
We can infer from the list above that the general sense of 未然形【みぜんけい】 verb stem + -しい seems to be "evoking the quality of the root verb".
As user4092 explained, the root of 忌々【いまいま】しい is not verb 忌【い】まう, but rather verb 忌【い】む "to avoid something (as unfortunate or taboo)". (For that matter, 忌【い】まう derives from the 未然形【みぜんけい】 of 忌【い】む + auxiliary verb ふ, which indicates repeated or ongoing action or state.) Given the meaning of the root verb, and the pattern of -しい adjective formation, we can arrive at the meaning of 忌々しい as "evoking a quality of avoidance, as of misfortune or taboo" → "detestable".
Reduplication of 未然形【みぜんけい】 verb stems in -しい adjectives, as in the formation of 忌々【いまいま】しい, seems to be quite unusual. A quick survey of my dictionaries to hand turns up various -しい adjectives based on reduplication, but none of them reduplicate the 未然形【みぜんけい】 verb stems of 五段活用【ごだんかつよう】 verbs (where the vowel on the end of the verb stem changes for each conjugation form; often called "Group 1", "five-row", or "quintigrade" in English). 忌【いま】しい without reduplication does exist in the historical record, but according to my dead-tree copy of Shogakukan's 国語大辞典【こくごだいじてん】, this appears in the Edo period and has already fallen out of use, while reduplicated 忌々【いまいま】しい appears much earlier in the Heian period, showing up in the 源氏物語【げんじものがたり】.
In conclusion, 忌々【いまいま】しい seems exceptional in its formation, but quite straightforward in its meaning and structure.
The bold above about 五段活用【ごだんかつよう】 verbs follows a helpful comment from macraf, pointing out the existence of other reduplicated-verb-root -しい adjectives for 一段活用【いちだんかつよう】 verbs (where the vowel on the end of the verb stem doesn't change for each conjugation form; often called "Group 2", "one-row", or "monograde" in English). Examples include:
The word it's based of is 忌む, which means to avoid (jinx). 忌々しい stands for such attribution as one wants to avoid.