If you have solved quadratic equations you have
met complex numbers. For example if you solve the
equation
you get the solutions x=2±√−9=2±3i
where i=√−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?