Kurs:Mathematik für Anwender (Osnabrück 2019-2020)/Teil I/Repetitorium/5/complex inverse/Studentenfrage

Is it correct that ${}-(x,y):=(-x,-y)$? Are they the inverse of ${}(x,y)$? How to proof ${}(-x,-y)$ is the inverse of ${}(x,y)$ using ${}a\cdot b=1$? (My proof got stuck.)

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