AS Further Maths - Complex Numbers

Sally Curtis, Sep 7, 2017

Table of Contents

  1. Lesson 2
    1. Imagining the roots of a quadratic equation
    2. Quadratic Equation: Complex Roots
  2. Lesson 4
    1. Adding complex numbers
    2. complex number addition
    3. complex number subtraction
    4. Arithmetic of complex numbers
  3. Lesson 5
    1. Modulus and argument
    2. Exploring Complex Numbers
    3. complex number operations
  4. Lesson 6
    1. Multiplying and dividing complex numbers
  5. Lesson 7
    1. Loci 1
    2. Loci 2
    3. Copy of Loci 3

1.

Lesson 2

Complex Conjugates

  • 1. Imagining the roots of a quadratic equation
  • 2. Quadratic Equation: Complex Roots

1.1.

Imagining the roots of a quadratic equation

The roots of a quadratic equation can be found symmetrically either side of the vertical line through the vertex. For a quadratic equation with complex roots this can be found by examining a parabola of the form y=–x² with the same vertex as the original curve.
– Tom Button

1.2.

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2.

Lesson 4

Looking at the argand diagram. What does addition and subtraction look like when adding complex number?

  • 1. Adding complex numbers
  • 2. complex number addition
  • 3. complex number subtraction
  • 4. Arithmetic of complex numbers

2.1.

Adding complex numbers

The complex numbers w and z can be moved by dragging.[br]Use the checkboxes to see the sum and difference of w and z.
– Integral Resources

2.2.

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2.3.

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2.4.

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3.

Lesson 5

Modulus and Argument form of Complex Numbers

  • 1. Modulus and argument
  • 2. Exploring Complex Numbers
  • 3. complex number operations

3.1.

Modulus and argument

Move the point to explore the modulus and argument of a complex number.[br]How do you calculate the argument when the complex number is in each quadrant?
– Integral Resources

3.2.

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3.3.

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4.

Lesson 6

Multiplying and dividing in modulus-argument form.

  • 1. Multiplying and dividing complex numbers

4.1.

Multiplying and dividing complex numbers

Move the points to explore what happens when you multiply or divide two complex numbers given in modulus-argument form.[br]What is happening geometrically?
– Integral Resources

5.

Lesson 7

Loci in the Complex plane

  • 1. Loci 1
  • 2. Loci 2
  • 3. Copy of Loci 3

5.1.

Loci 1

Move the blue point so that it satisfies the equation shown in green. Find as many positions as you can that satisfy the equation.[br]Use the checkbox to see the set of points that satisfy the equation. How can you describe this set of points?[br]You can move the point [i]a[/i] and change the value of [i]r[/i].
– Integral Resources

5.2.

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5.3.

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