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Further Maths: Core Pure -Edexcel-A Level

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  1. complex-numbers-and-argand-diagrams
    6 主题
  2. exponential-form-and-de-moivres-theorem
    4 主题
  3. properties-of-matrices
    3 主题
  4. transformations-using-matrices
    3 主题
  5. roots-of-polynomials
    2 主题
  6. series
    2 主题
  7. maclaurin-series
    1 主题
  8. hyperbolic-functions
    4 主题
  9. volumes-of-revolution
    2 主题
  10. methods-in-calculus
    5 主题
  11. vector-lines
    4 主题
  12. vector-planes
    4 主题
  13. polar-coordinates
    2 主题
  14. first-order-differential-equations
    3 主题
  15. second-order-differential-equations
    2 主题
  16. simple-harmonic-motion
    2 主题
  17. proof-by-induction
    2 主题
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Argand diagrams – basics

What is an Argand diagram?

  • An Argand diagram is a geometrical way to represent complex numbers as either a point or a vector in two-dimensional space

    • We can represent the complex number x plus y straight i by the point with cartesian coordinate left parenthesis x comma space y right parenthesis

  • The real component is represented by points on the x-axis, called the real axis, Re

  • The imaginary component is represented by points on the y-axis, called the imaginary axis, Im

8-2-1-argand-diagrams---basics-diagram-1
8-2-1-argand-diagrams---basics-diagram-2

  • You may be asked to show roots of an equation in an Argand diagram

    • First solve the equation

    • Draw a quick sketch, only adding essential information to the axes

    • Plot the points and label clearly

How can I use an Argand diagram to visualise |z1 + z2| and |z1 – z2|?

  • Plot two complex numbers z1 and z2

  • Draw a line from the origin to each complex number

  • Form a parallelogram using the two lines as two adjacent sides

  • The modulus of their sum |z1 + z2| will be the length of the diagonal of the parallelogram starting at the origin

  • The modulus of their difference |z1 – z2| will be the length of the diagonal between the two complex numbers

8-2-1-argand-diagram

Worked Example

a) Plot the complex numbers z1 = 2 + 2i  and z2 = 3 – 4i as points on an Argand diagram.

1-8-3-ib-hl-aa-argand-diagrams-we-a

b) Write down the complex numbers represented by the points A and B on the Argand diagram below.

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