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Die komplexen Zahlen

In: Lehrbuch der Funktionentheorie

Author

Listed:
  • Hans Hornich

    (Technischen Hochschule Graz)

Abstract

Zusammenfassung Daß eine quadratische Gleichung nicht stets eine Lösung in reellen Zahlen hat, ist schon sehr lange bekannt. Die ersten schüchternen Versuche mit Quadratwurzeln aus negativen Zahlen zu rechnen, beginnen mit H. Cardano vor etwa 400 Jahren. Erst allmählich schwindet die Scheu vor dem „Imaginären” und klären sich paradoxe Erscheinungen, die bei naiver Übertragung des Formelapparates vom Reellen ins Komplexe auftreten. Euler rechnet schon ganz selbstverständlich und sicher mit komplexen Zahlen; er führt die Bezeichnung $$i=\sqrt{-1}$$ ein. Die systematische Entwicklung der Theorie erfolgt endgültig durch Hamilton in rein arithmetischer, durch Gauß in geometrischer Darstellung.

Suggested Citation

  • Hans Hornich, 1950. "Die komplexen Zahlen," Springer Books, in: Lehrbuch der Funktionentheorie, chapter 0, pages 1-14, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-7739-6_1
    DOI: 10.1007/978-3-7091-7739-6_1
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