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#### Resources tagged with Complex numbers similar to Cube Roots:

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### Cube Roots

##### Stage: 5 Challenge Level:

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

### 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.

### 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?

### 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.

### Complex Countdown

##### Stage: 5 Challenge Level:

Play a more cerebral countdown using complex numbers.

### 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.

### 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?

### An Introduction to Complex Numbers

##### Stage: 5

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

### Footprints

##### Stage: 5 Challenge Level:

Make a footprint pattern using only reflections.

### 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. . . .

### Twizzle Twists

##### Stage: 4 Challenge Level:

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

### Three by One

##### Stage: 5 Challenge Level:

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

### 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?

### 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!

### Two and Four Dimensional Numbers

##### Stage: 5 Challenge Level:

Investigate matrix models for complex numbers and quaternions.

### 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?

### Interactive Workout - Further

##### Stage: 5 Challenge Level:

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

### 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.

### 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?

### 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?. . . .

### 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.

### 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?

### Pumping the Power

##### Stage: 5 Challenge Level:

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

### Impedance Can Be Complex!

##### Stage: 5 Challenge Level:

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

### Twizzles Venture Forth

##### Stage: 4 Challenge Level:

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