85
Bearbeitungen
Änderungen
→Gesetzmäßigkeiten
'''Komplexe Zahlen'''
'''Komplexe Zahlen'''
In den komplexen Zahlen gelten folgende Rechengesetze:
1)(x<sub>1</sub> + i • y<sub>1</sub>) + (x<sub>2</sub> + i • y<sub>2</sub>) = (x<sub>1</sub> + x<sub>2</sub>) + i • (y<sub>1</sub> + y<sub>2</sub>)
1) (x<sub>1</sub> + i • y<sub>1</sub>) + (x<sub>2</sub> + i • y<sub>2</sub>) = (x<sub>1</sub> + x<sub>2</sub>) + i • (y<sub>1</sub> + y<sub>2</sub>)
2)(x<sub>1</sub> + i • y<sub>1</sub>) - (x<sub>2</sub> + i • y<sub>2</sub>) = (x<sub>1</sub> - x<sub>2</sub>) + i • (y<sub>1</sub> - y<sub>2</sub>)
2) (x<sub>1</sub> + i • y<sub>1</sub>) - (x<sub>2</sub> + i • y<sub>2</sub>) = (x<sub>1</sub> - x<sub>2</sub>) + i • (y<sub>1</sub> - y<sub>2</sub>)
3)(x<sub>1</sub> + i • y<sub>1</sub>) • (x<sub>2</sub> + i • y<sub>2</sub>) = (x<sub>1</sub>x<sub>2</sub> - y<sub>1</sub>y<sub>2</sub>) + i • (x<sub>1</sub>y<sub>2</sub> + x<sub>2</sub>y<sub>1</sub>)
3) (x<sub>1</sub> + i • y<sub>1</sub>) • (x<sub>2</sub> + i • y<sub>2</sub>) = (x<sub>1</sub>x<sub>2</sub> - y<sub>1</sub>y<sub>2</sub>) + i • (x<sub>1</sub>y<sub>2</sub> + x<sub>2</sub>y<sub>1</sub>)
4)(x<sub>1</sub> + i • y<sub>1</sub>) / (x<sub>2</sub> + i • y<sub>2</sub>) = (x<sub>1</sub>x<sub>2</sub> + y<sub>1</sub>y<sub>2</sub>) / (x<sub>2</sub>²+ y<sub>2</sub>²) + i • (x<sub>2</sub>y<sub>1</sub> - x<sub>1</sub>y<sub>2</sub>) / (x<sub>2</sub>²+ y<sub>2</sub>²)
4) (x<sub>1</sub> + i • y<sub>1</sub>) / (x<sub>2</sub> + i • y<sub>2</sub>) = (x<sub>1</sub>x<sub>2</sub> + y<sub>1</sub>y<sub>2</sub>) / (x<sub>2</sub>²+ y<sub>2</sub>²) + i • (x<sub>2</sub>y<sub>1</sub> - x<sub>1</sub>y<sub>2</sub>) / (x<sub>2</sub>²+ y<sub>2</sub>²)
(Division nur im Falle von x<sub>2</sub> + i • y<sub>2</sub> ≠ 0)
=Zahlenbereiche im Mathematikunterricht=
=Zahlenbereiche im Mathematikunterricht=