Recent content by 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!

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...

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...

z^n = lcis(2pi/n) - 1l*cis theta ? and I guess theta would be equal to pi (n-2)/n (I guessed that from the rule for the interior angles of a polygon!)

So I can say that : z^n= r*lcis(2pi/n) - 1l ?

In case of n=4, we'll substitute the 5 for 4 and in case of n=3, we'll substitute the 5 for.. And for a general formula, we'll just put "n"... Ok, one last thing, I was told that the conjecture would be in the form of z=rcis something, and I can't relate that to the distance

I still can't formulate those findings into a conjecture I'm sorry... Thank you very much for your help.. I woulda never asked for better help!

Yeah, I do! Approx value 1.175570505?

0.021932

I do! I just did it with my calculator! It's supposed to be Sqrt ((cos2pi/5)^2 + (sin2pi/5)^2) It's sqrt1 :) :) So, they's sqrt1, sqrt2, and sqrt3 for z^5, z^4, and z^3, respectively! I can see a pattern: As the no of sides of the polygon increases by one, the distance between the roots...

Equals 1? the distance of (cos2pi/4, sin2pi/4) and (1,0): sqrt2 the distance of (cos2pi/3, sin2pi/3) and (1,0): sqrt3 No pattern that I can spot :/ I'm sorry!

Yes! (cos2pi/5, sin2pi/5) or cos72, sin72 But they give big numbers, and I can't put the results in a pattern with the other polygons

The three line segments are equal to sqrt3, right?

sqrt2?

I was talkin' about the bigger one between (1,0) (-1/2, sqrt3/2) and (-1/2, -sqrt3/2) About your traingle: It's a right angled traingle with angles: 90, 30 and 60.. Still no clue about the length