Complex numbers

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.

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?

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.

Make a footprint pattern using only reflections.

Investigate x to the power n plus 1 over x to the power n when x plus 1 over x equals 1.

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?