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Resources tagged with Complex numbers similar to Belt:

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Broad Topics > Advanced Algebra > Complex numbers

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Three by One

Stage: 5 Challenge Level: Challenge Level:1

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

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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. . . .

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Complex Sine

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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8 Methods for Three by One

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

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?. . . .

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Complex Countdown

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Play a more cerebral countdown using complex numbers.

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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.

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An Introduction to Complex Numbers

Stage: 5

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

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Conjugate Tracker

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Complex Partial Fractions

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

To break down an algebraic fraction into partial fractions in which all the denominators are linear and all the numerators are constants you simetimes need complex numbers.

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Sheep in Wolf's Clothing

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Pumping the Power

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Thousand Words

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Footprints

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Make a footprint pattern using only reflections.

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Cube Roots

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Complex Rotations

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Two and Four Dimensional Numbers

Stage: 5 Challenge Level: Challenge Level:1

Investigate matrix models for complex numbers and quaternions.

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Target Six

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Napoleon's Theorem

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Roots and Coefficients

Stage: 5 Challenge Level: Challenge Level:1

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?

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Twizzle Wind Up

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Twizzle Twists

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Thebault's Theorem

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Interactive Workout - Further

Stage: 5 Challenge Level: Challenge Level:1

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

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Sextet

Stage: 5 Challenge Level: Challenge Level:1

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

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Twizzles Venture Forth

Stage: 4 Challenge Level: Challenge Level:1

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

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Impedance Can Be Complex!

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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