4VD-H6 Complexe getallen

Carolijn Tacken, May 11, 2014

vermenigvuldigen, delen, machtsverheffen e.d.

Table of Contents

  1. Rekenen met complexe getallen
    1. Vermenigvuldigen van complexe getallen: kwadraten
    2. Vermenigvuldigen van complexe getallen
    3. Delen van complexe getallen
    4. Machten van z (stelling van de Moivre)
    5. Complex worteltrekken
  2. What's my rule?
    1. Complex Numbers: What's My Rule?
    2. Complex Numbers: What's My Rule?
    3. Complex Numbers: What's My Rule?
    4. Complex Numbers: What's My Rule?
    5. Complex Numbers: What's My Rule?
    6. Complex Numbers: What's My Rule?
    7. Complex Numbers: What's My Rule?
    8. Complex Numbers: What's My Rule?
    9. Complex Numbers: What's My Rule?

1.

Rekenen met complexe getallen

  • 1. Vermenigvuldigen van complexe getallen: kwadraten
  • 2. Vermenigvuldigen van complexe getallen
  • 3. Delen van complexe getallen
  • 4. Machten van z (stelling van de Moivre)
  • 5. Complex worteltrekken

1.1.

Vermenigvuldigen van complexe getallen: kwadraten

In de applet hieronder zijn het punt (complexe getal) [math]z_1[/math] en zijn kwadraat [math]z[/math] getekend. Versleep het punt [math]z_1[/math] en kijk wat er gebeurt. Beantwoord de volgende vragen. [list=1] [*]Voor welke getallen [math]z_1[/math] geldt dat het kwadraat, dus het punt [math]z[/math], op de reële as terecht komt? [*]En voor welke getallen [math]z_1[/math] komt het kwadraat op de imaginaire as terecht? [*]Welk verband is er tussen het argument van [math]z_1[/math] en dat van [math]z[/math]? [*]Welk verband is er tussen de moduli van [math]z_1[/math] en [math]z[/math]? [/list]
– Carolijn Tacken

1.2.

–

1.3.

–

1.4.

–

1.5.

–

2.

What's my rule?

  • 1. Complex Numbers: What's My Rule?
  • 2. Complex Numbers: What's My Rule?
  • 3. Complex Numbers: What's My Rule?
  • 4. Complex Numbers: What's My Rule?
  • 5. Complex Numbers: What's My Rule?
  • 6. Complex Numbers: What's My Rule?
  • 7. Complex Numbers: What's My Rule?
  • 8. Complex Numbers: What's My Rule?
  • 9. Complex Numbers: What's My Rule?

2.1.

Complex Numbers: What's My Rule?

Points A and C are complex numbers. Drag point A. Point C moves in response. What is the rule that defines points C? Try to describe it geometrically and algebraically. Is it possible to move A without moving C? Is it possible to move A so point C is at the origin? What happens to C when A moves along the Real axis? What happens to C when A moves along the Imaginary axis? Is it possible to move A so point C moves along the Real axis? Is it possible to move A so point C moves along the Imaginary axis?
– Steve Phelps, Carolijn Tacken

2.2.

–

2.3.

–

2.4.

–

2.5.

–

2.6.

–

2.7.

–

2.8.

–

2.9.

–

Information