Complex numbers

There are 22 NRICH Mathematical resources connected to Complex numbers
8 Methods for Three By One
problem
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8 methods for three by one

Age
14 to 18
Challenge level
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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? Which do you like best?
Three by One
problem
Favourite

Three by one

Age
16 to 18
Challenge level
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There are many different methods to solve this geometrical problem - how many can you find?
Complex partial fractions
problem
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Complex partial fractions

Age
16 to 18
Challenge level
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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.
Footprints
problem

Footprints

Age
16 to 18
Challenge level
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Make a footprint pattern using only reflections.
Sextet
problem

Sextet

Age
16 to 18
Challenge level
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Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.
Pumping the Power
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Pumping the power

Age
16 to 18
Challenge level
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What is an AC voltage? How much power does an AC power source supply?
Impedance can be complex!
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Impedance can be complex!

Age
16 to 18
Challenge level
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Put your complex numbers and calculus to the test with this impedance calculation.
Sheep in wolf's clothing
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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
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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?