Complex numbers

There are 22 NRICH Mathematical resources connected to Complex numbers

problem

Cube Roots

Age

16 to 18

Challenge level

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

problem

Napoleon's Theorem

Age

14 to 18

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?

problem

Complex Rotations

Age

16 to 18

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?

problem

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?

problem

Target Six

Age

16 to 18

Challenge level

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

problem

Roots and Coefficients

Age

16 to 18

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?

article

Challenge level

What happens when we multiply a complex number by a real or an imaginary number?

Or search by topic

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners

Complex numbers

Cube Roots

Napoleon's Theorem

Complex Rotations

8 Methods for Three By One

Target Six

Roots and Coefficients

What Are Numbers?

What are Complex Numbers?

An introduction to complex Numbers

Strolling along