Search by Topic

Resources tagged with Complex numbers similar to Two and Four Dimensional Numbers:

Filter by: Content type:
Stage:
Challenge level:

Two and Four Dimensional Numbers

Stage: 5 Challenge Level:

Investigate matrix models for complex numbers and quaternions.

Twizzle Twists

Stage: 4 Challenge Level:

Make the twizzle twist on its spot and so work out the hidden link.

8 Methods for Three by One

Stage: 4 and 5 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?. . . .

Twizzle Wind Up

Stage: 4 Challenge Level:

A loopy exploration of z^2+1=0 (z squared plus one) with an eye on winding numbers. Try not to get dizzy!

Footprints

Stage: 5 Challenge Level:

Make a footprint pattern using only reflections.

An Introduction to Complex Numbers

Stage: 5

A short introduction to complex numbers written primarily for students aged 14 to 19.

Sheep in Wolf's Clothing

Stage: 5 Challenge Level:

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

Complex Countdown

Stage: 5 Challenge Level:

Play a more cerebral countdown using complex numbers.

What Are Complex Numbers?

Stage: 5

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. . . .

Complex Rotations

Stage: 5 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?

Thebault's Theorem

Stage: 5 Challenge Level:

Take any parallelogram and draw squares on the sides of the parallelogram. What can you prove about the quadrilateral formed by joining the centres of these squares?

Three by One

Stage: 5 Challenge Level:

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

Complex Partial Fractions

Stage: 5 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.

What Are Numbers?

Stage: 2, 3, 4 and 5

Ranging from kindergarten mathematics to the fringe of research this informal article paints the big picture of number in a non technical way suitable for primary teachers and older students.

Conjugate Tracker

Stage: 5 Challenge Level:

Make a conjecture about the curved track taken by the complex roots of a quadratic equation and use complex conjugates to prove your conjecture.

Sextet

Stage: 5 Challenge Level:

Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.

Cube Roots

Stage: 5 Challenge Level:

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

Roots and Coefficients

Stage: 5 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?

Napoleon's Theorem

Stage: 4 and 5 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?

Interactive Workout - Further

Stage: 5 Challenge Level:

Give your further pure mathematics skills a workout with this interactive and reusable set of activities.

Twizzles Venture Forth

Stage: 4 Challenge Level:

Where we follow twizzles to places that no number has been before.

Impedance Can Be Complex!

Stage: 5 Challenge Level:

Put your complex numbers and calculus to the test with this impedance calculation.

Pumping the Power

Stage: 5 Challenge Level:

What is an AC voltage? How much power does an AC power source supply?

Complex Sine

Stage: 5 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.

Target Six

Stage: 5 Challenge Level:

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

Thousand Words

Stage: 5 Challenge Level:

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