You may also like

problem icon

8 Methods for Three by One

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?

problem icon

Napoleon's Theorem

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 icon

Twizzle Wind Up

A loopy exploration of z^2+1=0 (z squared plus one) with an eye on winding numbers. Try not to get dizzy!

Twizzles Venture Forth

Stage: 4 Challenge Level: Challenge Level:1

Remember that i is the name of the twizzle that has a number arrow equal to the unit arrow rotated through 90 degrees.

In other words i = 1 cis 90 .

The twizzle multiplication rule is neatly expressed by saying 'Multiply the number arrow lengths, and add the angles'.

So $i^2 = i \times i= 1 cis 90 \times 1 cis 90 = 1 cis 180 = -1.$ Now you should have enough information to multiply out (z-i)(z+i) .