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Contents
- Whole Topic Notes
- 3A Loci in an Argand Diagram
- 3B Regions in an Argand Diagram
- 3C Transformations of the Complex Plane*
- Whole Topic Summary Resources (Including Past Paper Questions)
Whole Topic Notes
Full Notes to Accompany Examples
Dr Frost
- Dr Frost Further Pure 2 Complex Numbers Section
3A Loci in an Argand Diagram
Textbook resources
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Dr Frost resources
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Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 804a: Determine the Cartesian equations for locus given in the form \left|z-a\right| = k\left|z – b\right|
- 804b: Sketch the locus for equations given in the form \left|z-a\right| = k\left|z – b\right|
- 804c: Determine the minimum and maximum values of \textrm{arg}(z) for a locus given in the form \left|z-a\right| = k\left|z – b\right|
- 804d: Determine the minimum and maximum values of \left|z\right| for a locus given in the form \left|z-a\right| = k\left|z – b\right|
- 804e: Determine a complex number which satisfies both \left|z-a\right| = k\left|z – b\right| and arg(z-c) = \theta
- 804f: Sketch the locus for equations given in the form arg\left( \frac{z-a}{z-b} \right) = \beta
- 804g: Identify the minimum or maximum value of \left|z\right| given a locus given in the form arg\left( \frac{z-a}{z-b} \right) = \beta
- 804: Exam Practice: More complex loci in an Argand diagram
3B Regions in an Argand Diagram
Textbook resources
No Video Yet
Dr Frost resources
No Live Lesson Video Yet
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
3C Transformations of the Complex Plane*
Textbook resources
No Video Yet
Dr Frost resources
No Live Lesson Video Yet
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 805a: Determine the complex equation of a locus given a transformation w = f(z) (with simple changing of subject).
- 805b: Determine the complex equation of a locus given a transformation w = f(z) (with more complex changing of subject).
- 805c: Determine the Cartesian equation of a curve formed by applying a transformation w = f(z) to a horizontal or vertical line.
- 805d: Describe the geometric transformation from one locus to another given a transformation w = f(z).
- 805e: Apply a Mobius transformation w = \frac{az + b}{cz + d} to a circle in the z-plane.
- 805f: Apply a Mobius transformation w = \frac{az + b}{cz + d} to a straight line in the z-plane.
- 805: Exam Practice: Elementary transformations from one complex plane to another
Worksheets
- Mathshelper (Jon Stone)