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Resources tagged with Complex numbers similar to An Introduction to Complex Numbers:

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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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Two and Four Dimensional Numbers

Stage: 5 Challenge Level: Challenge Level:1

Investigate matrix models for complex numbers and quaternions.

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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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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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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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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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Footprints

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

Make a footprint pattern using only reflections.

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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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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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Cubic Tracker

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

Explore changes in solutions to cubic equations as you change the graph of the cubic polynomial. Track the real and complex roots.

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Root Tracker

Stage: 5 Challenge Level: Challenge Level:1

Track the roots of quadratic equations as you move the corresponding graphs and discover the transitions from real to complex roots.

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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: 5

Two 18 year old students from Madras College St Andrews in Scotland produced eight different proofs of one result using (separately) Tan Angle Sum Formula, Sin Angle Sum Formula, Cosine Rule,. . . .

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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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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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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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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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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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Three by One

Stage: 5 Challenge Level: Challenge Level:1

NRICH has always had good solutions from Madras College in St Andrew's, Scotland but the solutions to this problem were truly exceptional.

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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 explain why this is so. Find all the solutions of the equation.

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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?