### There are 21 results

Broad Topics >

Numbers and the Number System > Complex numbers

##### 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.

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

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

##### 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.

##### Age 16 to 18 Challenge Level:

Investigate matrix models for complex numbers and quaternions.

##### Age 16 to 18 Challenge Level:

Play a more cerebral countdown using complex numbers.

##### Age 7 to 18

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.

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18

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. . . .

##### Age 16 to 18 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.

##### Age 16 to 18

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

##### Age 16 to 18 Challenge Level:

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

##### 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?. . . .

##### Age 16 to 18 Challenge Level:

Make a footprint pattern using only reflections.

##### 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?

##### 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?

##### Age 16 to 18 Challenge Level:

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

##### 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.

##### 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?

##### Age 16 to 18 Challenge Level:

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

##### 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.