eksiĝi

Decode it and it is funny. Eks- is the prefix you already know from eksedzo, an ex-husband, and eksprezidanto, a former president. -Iĝ- is the suffix for becoming: ruĝa red, ruĝiĝi to go red. Bolt them together with no root in between and you get eksiĝi, to become an ex. Esperanto lets a prefix and a suffix shake hands with nothing between them and treats the result as an ordinary verb, which is the sort of thing the language does casually and no national language can do at all. English needs five words for it.

The precedent is already in the course. Eksedziĝi at rank 2,299 is to get divorced, and it is built the same way with edzo in the middle: to become an ex-spouse. Once you have seen that, eksiĝi is not a new word to memorise, it is the same machine with the middle taken out. The transitive partner is eksigi, which arrived at rank 2,940 with -ig- in place of -iĝ-: to make somebody an ex, which is to sack them. The difference between eksiĝis and estis eksigita is the difference between resigning and being pushed.

And the fence with demisii. Demisii at 2,427 means exactly the same thing, and the two are a set piece in the argument Esperanto has with itself. Demisii is a French loan, transparent to anyone who knows French and opaque to everyone else. Eksiĝi is built from parts every beginner already owns, and the Reta Vortaro gently prefers it. In practice the Esperanto press uses demisii constantly, so you will read both; write whichever you like, but know that choosing eksiĝi is a small vote for the affix system. Eksiĝo is the resignation itself.