Complex numbers

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?

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

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.

Matrices and Complex Numbers combine to enable us to create four dimensional numbers.

What is an AC voltage? How much power does an AC power source supply?

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

Can you work out what simple structures have been dressed up in these advanced mathematical representations?

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?

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

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?