If you have solved quadratic equations you have met complex numbers. For example if you solve the equation

x2-4x+13=0

you get the solutions

x=2±

__ Ö-9

=2±3i

where

i=

__ Ö-1

.

The complex number a+ib is represented in the plane by the point with coordinates (a,b). This is called an Argand diagram. Make your own choice of some complex numbers, and mark them on a graph with lines joining the points to the origin. Now multiply your numbers by -1 and join their images to the origin. Make and prove a conjecture about the geometric effect of multiplying complex numbers by -1.

Again make a choice of some complex numbers and multiply each one by i. Draw the complex numbers and their images on a graph and make and prove a conjecture about the effect of multiplying complex numbers by i.

What happens if you multiply a complex number by i twice, three times, four times, ..., n times?