Other tags that relate to Proof Sorter - the Square Root of 2 Is Irrational
Rational and irrational numbers. Interactivities. Arithmetic sequences. Mathematical reasoning & proof. Surds. Video. Integers. Complex numbers. Proof by contradiction. Coordinates.There are 20 results
Broad Topics > Numbers and the Number System > Complex numbers
What Are Numbers?
Age 7 to 18
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.
Conjugate Tracker
Age 16 to 18 Challenge Level:
Make a conjecture about the curved track taken by the complex roots of a quadratic equation and use complex conjugates to prove your conjecture.
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?
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.
Complex Sine
Age 16 to 18 Challenge Level:
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.
An Introduction to Complex Numbers
Age 16 to 18
A short introduction to complex numbers written primarily for students aged 14 to 19.
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?
Cube Roots
Age 16 to 18 Challenge Level:
Evaluate without a calculator: (5 sqrt2 + 7)^{1/3} - (5 sqrt2 - 7)^1/3}.
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?
Sheep in Wolf's Clothing
Age 16 to 18 Challenge Level:
Can you work out what simple structures have been dressed up in these advanced mathematical representations?
8 Methods for Three by One
Age 14 to 18 Challenge Level:
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?. . . .
Three by One
Age 16 to 18 Challenge Level:
There are many different methods to solve this geometrical problem - how many can you find?
Two and Four Dimensional Numbers
Age 16 to 18 Challenge Level:
Investigate matrix models for complex numbers and quaternions.
Complex Partial Fractions
Age 16 to 18 Challenge Level:
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.
What Are Complex Numbers?
Age 16 to 18
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. . . .
Sextet
Age 16 to 18 Challenge Level:
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
Age 16 to 18 Challenge Level:
What is an AC voltage? How much power does an AC power source supply?
Impedance Can Be Complex!
Age 16 to 18 Challenge Level:
Put your complex numbers and calculus to the test with this impedance calculation.
NRICH is part of the family of activities in the Millennium Mathematics Project.