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# need help on FP2 - complex numbers watch

1. there is 1 question and an example, in the fp2 edexcel book, asking us to find the equation of a circle with points w on its circumference, generally looking like this:

w^3=-1

do the cubed roots of unity always make a circle centre 0,0 ?

and what is the 'roots of unity' jargon ?

thanks
2. (Original post by Andamiriel)
...
Might be useful:

http://www.maths.abdn.ac.uk/~igc/tch...s/node101.html

The article in Wikipaedia is a bit OTT for A-level.
3. An "nth root of unity" is a number which, to the nth power, equals 1. Note that you can write for any integer value of k , and so if then . Numbers of this form are the roots of unity.

Why must they lie on the unit circle? Well if and then what is ? So what is ? (Considering that r is a positive real number you're fairly limited to what it can be).

In this case you have , so you can proceed in a similar way, but be careful with that minus sign. Or alternatively notice that and go about it that way (which is probably easier).
4. the cubed roots of unity are the complex numbers z such that z^3 = 1. So obviously 1 is one, but there are 2 others (there are n nth roots of unity).

These do always lie on a circle centred around (0,0) with a radius of 1. So, all you have to do is find the z so that z^3 = -1 (this is the same as finding the cubed roots of unity called (-z)) and show that they satisfy the equation of a circle radius one on the origin.
5. right thanks for clearing that up

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