IBMathsDPAnalysis & Approaches (AA)HLRevision Notes1. Number & AlgebraComplex NumbersIntroduction to Argand Diagrams

Introduction to Argand Diagrams (DP IB Analysis & Approaches (AA)): Revision Note

Amber

Written by: Amber

Reviewed by: Mark Curtis

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DP Analysis & Approaches (AA): HLDP Applications & Interpretation (AI): HL

Argand diagrams

What is the complex plane?

  • The complex plane (also know as the Argand plane) is a 2D grid used to illustrated complex numbers

    • It is similar to 2D Cartesian coordinates

      • The x-axis is known as the real axis (Re)

      •  The y-axis is known as the imaginary axis (Im)

What is an Argand diagram?

  • An Argand diagram is a geometrical representation of complex numbers on a complex plane

  • The complex number z equals x plus y straight i is represented

    • either by the point open parentheses x comma space y close parentheses

    • or by the vector from open parentheses 0 comma space 0 close parentheses to open parentheses x comma space y close parentheses

      • with an arrow pointing away from the origin

Graph showing complex numbers z=2+6i and w=5+i. The imaginary part is on the vertical axis, real part on the horizontal axis.

Examiner Tips and Tricks

When asked to sketch an Argand diagram, you do not need to draw a grid and plot each point (a rough sketch showing the correct features is fine).

Worked Example

(a) Sketch the complex numbers z subscript 1 equals 2 plus 2 straight i and z subscript 2 equals 3 minus 4 straight i 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.

we-diagram-argand-diagrams
1-8-3-ib-hl-aa-argand-diagrams-we-b

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    Amber

    Author: Amber

    Expertise: Maths Content Creator

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.

    Mark Curtis

    Reviewer: Mark Curtis

    Expertise: Maths Content Creator

    Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.