They're probably similar in meaning, but complicacy sounds/looks ugly compared to complexity if you are using them in the same way. The word complication can also refer to knock-on effects of complexity, in a way that complex doesn't do. d
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MUSCOVITEthese two wordsUntil today, when I had to look it up to be sure it was even a word, I had never heard of the word "complicacy". In fact, my spell checker underlines it as a misspelled word even though it can be found in a dictionary.
MUSCOVITEAnother funny example - the dictionary has an entry for "eiderdown" (=comforter) but completely ignores "comforter" and "duvet".In the early 1960s very few British people had heard of a duvet. We had sheets, blankets, an eiderdown and a bedspread on our beds.
MUSCOVITEfamily heirloomKeep the heirloom, but get a new dictionary or use what you can find on-line.