Complex numbers

  • Strolling along
    problem

    Strolling Along

    Age
    14 to 18
    Challenge level

    What happens when we multiply a complex number by a real or an imaginary number?

  • Napoleon's Theorem
    problem

    Napoleon's Theorem

    Age
    14 to 18
    Challenge level

    Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?

  • Two and Four Dimensional Numbers
    problem

    Two and Four Dimensional Numbers

    Age
    16 to 18
    Challenge level

    Matrices and Complex Numbers combine to enable us to create four dimensional numbers.

  • Target Six
    problem

    Target Six

    Age
    16 to 18
    Challenge level

    Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.

  • Cube Roots
    problem

    Cube Roots

    Age
    16 to 18
    Challenge level

    Evaluate without a calculator: (5 sqrt2 + 7)^{1/3} - (5 sqrt2 - 7)^1/3}.

  • Thousand Words
    problem

    Thousand Words

    Age
    16 to 18
    Challenge level

    Here the diagram says it all. Can you find the diagram?

  • Sheep in wolf's clothing
    problem

    Sheep in Wolf's Clothing

    Age
    16 to 18
    Challenge level

    Can you work out what simple structures have been dressed up in these advanced mathematical representations?

  • What are Complex Numbers?
    article

    What Are Complex Numbers?

    This article introduces complex numbers, brings together into one bigger 'picture' some closely related elementary ideas like vectors and the exponential and trigonometric functions and their derivatives and proves that e^(i pi)= -1.
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