Roots of unity - complex no. (1 Viewer)

[Joshmosh2]

For the argument component, it is stated that theta = 2kpi / n

For example, if z^3 = 1, the arguments are 0, 2pi/3 and 4pi/3

What happens to negative numbers, such as z^3 = -1?
Is it the same thing, but for odd numbers such as
pi/3 , pi, 5pi/3?

Thanks.

 

[Axio]

Yes, that's it. You simply place the first root at (-1,0) and the roots are equally spaced out from there.

 

[Carrotsticks]

Correct, except remember to take into account principle arguments ie: 4pi/3 should be -2pi/3.

 

[braintic]

Correct, except remember to take into account principle arguments ie: 4pi/3 should be -2pi/3.

HSC markers don't care about principal arguments (unless of course it is a 'show' question).

 

[Carrotsticks]

HSC markers don't care about principal arguments (unless of course it is a 'show' question).

They don't, but I know that a great deal of school teachers do when marking internal assessments.

Also, it plays a purpose in these problems because emphasises the conjugate root theorem.

 

[Axio]

I would start another thread, but this does have to do with complex numbers...

How often should I be using the complex numbers mode on my calculator to solve things that have 'i' in them, do the markers want to see all of the calculation steps when for example you are finding remainders by subbing in something like 'i' into P(x)?