Complex getallen

Sjabloon:Manual Page

GeoGebra Objecten

• Meetkundige Objecten
• Algemene Objecten
  • Getallen en hoeken
  • Complexe getallen
  • Booleaanse waarden
  • Lijsten
  • Matrices
  • Teksten
  • Afbeeldingen
• Actie objecten
• Eigenschappen van object
• Vrije, afhankelijke en hulpobjecten
• Objecten benoemen
• Labels en titels
• Selecteer objecten
• Verander waarden
• Animatie
• Spoor
• Geavanceerde functies
• Scripting

GeoGebra does not support complex numbers directly, but you may use points to simulate operations with complex numbers.

Voorbeeld: If you enter the complex number 3 + 4ί into the Input Bar, you get the point (3, 4) in the Graphics View. This point’s coordinates are shown as 3 + 4ί in the Algebra View.

Nota: You can display any point as a complex number in the Algebra View. Open the Properties Dialog for the point and select Complex Number from the list of Coordinates formats on tab Algebra.

The imaginary unit ί can be chosen from the symbol box in the input bar or written using Sjabloon:KeyCode. Unless you are typing the input in CAS View or you defined variable i previously, variable i is recognized as the ordered pair i = (0, 1) or the complex number 0 + 1ί. This also means, that you can use this variable i in order to type complex numbers into the Input Bar (e. g., q = 3 + 4i), but not in the CAS.

Nota: The usual multiplication (2, 1)*(1, -2) gives you the scalar product of the two vectors.

The following commands and predefined operators can also be used:

• x(w) or real(w) return the real part of the complex number w
• y(w) or imaginary(w) return the imaginary part of the complex number w
• abs(w) or Length[w] return the absolute value of the complex number w
• arg(w) or Angle[w] return the argument of the complex number w
• conjugate(w) or Reflect[w,xAxis] return the conjugate of the complex number w

GeoGebra also recognizes expressions involving real and complex numbers. Sjabloon:Examples