Complex numbers

There are 22 NRICH Mathematical resources connected to Complex numbers
Sheep in wolf's clothing
problem

Sheep in wolf's clothing

Age
16 to 18
Challenge level
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Can you work out what simple structures have been dressed up in these advanced mathematical representations?
Roots and Coefficients
problem

Roots and coefficients

Age
16 to 18
Challenge level
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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?
Target Six
problem

Target six

Age
16 to 18
Challenge level
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Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.
Complex Rotations
problem

Complex rotations

Age
16 to 18
Challenge level
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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?
Napoleon's Theorem
problem

Napoleon's theorem

Age
14 to 18
Challenge level
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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?
Cube Roots
problem

Cube roots

Age
16 to 18
Challenge level
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Evaluate without a calculator: (5 sqrt2 + 7)^{1/3} - (5 sqrt2 - 7)^1/3}.
Opening the door
problem

Opening the door

Age
14 to 18
Challenge level
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What happens when we add together two complex numbers?
Strolling along
problem

Strolling along

Age
14 to 18
Challenge level
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What happens when we multiply a complex number by a real or an imaginary number?
What are Complex Numbers?
article

What are complex numbers?

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 their derivatives and proves that e^(i pi)= -1.