Patterns from complex numbers

[I like Serena]

Huh?

I really don't get what you intend with your formula.
Can you explain?

 

[Matricaria]

I mean, the original formula is: z=rcis theta
where r is the modulus and theta is the argument (For any complex number)..
YOu told me that we were going to substitute r for the distance between one root to another using the formula you helped me with..

So, I thought theta would be the interior angles of that polygon, ie the angle between each two sides..

 

[I like Serena]

No, I didn't intend for you to substitute r.

Your original formula defines the relation between any complex number z, and its distance to the origin r, and its angle theta.

However, your problem statement asks for the "distance" between different roots.
So as I see it, you need a formula that calculates a "distance" - not some complex number z.

What were you calculating?

 

[Matricaria]

This is the problem!
- Use de moivre's theorem to obtain solutions for z^3-1=0
- Use graphing software to plot these roots on an argand diagram as well as a unit circle with centre origin.
- Choose a root and draw line segments from this root to the other two roots.
- Measure these line segments and comment on your results.
Repeat the above for the quations z^4-1=0 and z^5-1=0. Comment on you results and try to formulate a conjecture.

Now all of it is done! I just need to formulate a conjecture which I can't!

 

[I like Serena]

Let's see what we can say.


z^n=1 has n roots given by z=cis(k 2pi/n), where k is the number 0, 1, ..., n-1.


The distance between 2 neighboring roots is |cis2pi/n - 1|.



However, I'm afraid this is not a conjecture, but just fact. ;)

 

[Matricaria]

Thank you very much!
I wouldn't ask for more :)

I'll work on the conjecture and let you know when I come up with something..

Thank you very much once again..
Have a great day!

 

[j.n]

i was just wondering if you found a conjecture for this? b/c i have to do this and i can't figure it out!
would it be |cis2pi/n - 1|?

thank-you so much!

 

[musicforlife]

Did you figure out the conjecture? i have NOO idea what to do

 

[musicforlife]

Hey. I am assuming you are done, and i happen to have the same topic now. Help with the conjecture , please ? :)