Complex numbers

problem
Pumping the power

Age

16 to 18

Challenge level

What is an AC voltage? How much power does an AC power source supply?
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
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.
problem
Impedance can be complex!

Age

16 to 18

Challenge level

Put your complex numbers and calculus to the test with this impedance calculation.
list
Adventures with complex numbers

Age

14 to 18

This collection is designed to give an introductory taste of complex numbers.
problem
Opening the door

Age

14 to 18

Challenge level

What happens when we add together two complex numbers?
problem
Strolling along

Age

14 to 18

Challenge level

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

Age

16 to 18

Challenge level

There are many different methods to solve this geometrical problem - how many can you find?
problem
Cube roots

Age

16 to 18

Challenge level

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