Complex numbers

  • Complex partial fractions
    problem
    Favourite

    Complex Partial Fractions

    Age
    16 to 18
    Challenge level
    To break down an algebraic fraction into partial fractions in which all the denominators are linear and all the numerators are constants you sometimes need complex numbers.
  • 8 Methods for Three By One
    problem
    Favourite

    8 Methods for Three by One

    Age
    14 to 18
    Challenge level

    This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different? Which do you like best?

  • Three by One
    problem
    Favourite

    Three by One

    Age
    16 to 18
    Challenge level

    There are many different methods to solve this geometrical problem - how many can you find?

  • Roots and Coefficients
    problem

    Roots and Coefficients

    Age
    16 to 18
    Challenge level
    If xyz = 1 and x+y+z =1/x + 1/y + 1/z show that at least one of these numbers must be 1. Now for the complexity! When are the other numbers real and when are they complex?
  • Sextet
    problem

    Sextet

    Age
    16 to 18
    Challenge level
    Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.
  • Complex Rotations
    problem

    Complex Rotations

    Age
    16 to 18
    Challenge level
    Choose some complex numbers and mark them by points on a graph. Multiply your numbers by i once, twice, three times, four times, ..., n times? What happens?
  • Footprints
    problem

    Footprints

    Age
    16 to 18
    Challenge level
    Make a footprint pattern using only reflections.
  • Pumping the Power
    problem

    Pumping the Power

    Age
    16 to 18
    Challenge level
    What is an AC voltage? How much power does an AC power source supply?
  • Complex Sine
    problem

    Complex Sine

    Age
    16 to 18
    Challenge level
    Solve the equation sin z = 2 for complex z. You only need the formula you are given for sin z in terms of the exponential function, and to solve a quadratic equation and use the logarithmic function.
  • Impedance can be complex!
    problem

    Impedance Can Be Complex!

    Age
    16 to 18
    Challenge level
    Put your complex numbers and calculus to the test with this impedance calculation.
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