# Resources tagged with: Complex numbers

### There are 19 results

Broad Topics >

The Number System and Place Value > Complex numbers

##### 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

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 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

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

##### Age 16 to 18

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

##### 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

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

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

Investigate matrix models for complex numbers and quaternions.

##### Age 16 to 18

Challenge Level

Make a footprint pattern using only reflections.

##### Age 16 to 18

Challenge Level

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

##### 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

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

##### 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

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 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.