CIE A Level Maths: Pure 3复习笔记8.2.4 Loci in Argand Diagrams

Loci in Argand Diagrams

How do I sketch the locus of or on an Argand diagram?

  • All complex numbers,, that satisfy the equation lie on a vertical line with Cartesian equation
    • Any complex number along this vertical line will have a real part of
  • All complex numbers, , that satisfy the equation lie on a horizontal line with Cartesian equation
    • Any complex number along this horizontal line will have an imaginary part of
  • E.g. The loci and are represented by the vertical line and the horizontal line

8-2-4_notes_fig1

Sketching the loci of and

8-2-4_notes_fig2

8-2-4_notes_fig3

8-2-4_notes_fig4

Worked Example

8-2-4_example_fig1-part-1

8-2-4_example_fig1-part-2

Exam Tip

  • In the exam, do not worry about making your diagrams perfect.
  • A quick sketch with all the key features is sufficient.

转载自savemyexams

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