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## 'Twizzles Venture Forth' printed from http://nrich.maths.org/

In this animation, the you can change the value of the blue twizzle

z . The red twizzle takes
the value

(z-i) . The
green twizzle takes the value

(z+i) . The grey twizzle takes the
value

(z-i)(z+i) . You can
check that by multiplying the red and green twizzles using

Twizzle Arithmetic . You need to know that

i is the name we give the twizzle
which has a number arrow equal to the unit arrow but rotated
through 90 degrees.

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There are lots of things to investigate with this animation, and
lots of things to think about...

Which values of the blue twizzle make the grey twizzle equal to
zero?

When you set the blue twizzle to one of these values, what happens
to the red and green twizzles?

When the grey twizzle is zero,

(z-i)(z+i)=0 . This should suggest to
you the two values of

z
for which this is true. Multiply out the expression

(z-i)(z+i) and so write the equation
in a simpler form.

Explain why you can't solve this equation using ordinary
numbers.

If you get stuck, look at the

hints. Before you progress to

Twizzle Wind Up, look at the

notes.