# Thread: Roots of complex numbers

1. ## Roots of complex numbers

Hello,

I need to find the relationship bewteen the power (n) in the equation : Z^n = a+bi , where |a+bi|=1 ...is it possible ? (Something other than De Moiver's theorem).

Thanks.

2. ## Re: Roots of complex numbers

Originally Posted by Hyunqul
I need to find the relationship bewteen the power (n) and what?
You do not have a compete thought there.

3. ## Re: Roots of complex numbers

Oh sorry , I missed that :

the relation bewteen the power (n) in the equation : Z^n = a+bi and the roots of Z (Solutions to the equation) , where |a+bi|=1 .... I need a general pattern relating them.

4. ## Re: Roots of complex numbers

Originally Posted by Hyunqul
the relation bewteen the power (n) in the equation : Z^n = a+bi and the roots of Z (Solutions to the equation) , where |a+bi|=1 .... I need a general pattern relating them.
1) there are n distinct complex numbers that satisfy that equation.

2) each one is point on the unit circle.

3) they create n arcs of equal measure, $\displaystyle \frac{2\pi}{n}$.

5. ## Re: Roots of complex numbers

and there's no other mathematical relationship or pattern between them?

6. ## Re: Roots of complex numbers

Originally Posted by Hyunqul
and there's no other mathematical relationship or pattern between them?
Why don't you investigate that?

7. ## Re: Roots of complex numbers

so if I started with adding the roots of an equation of Z^n=a+bi , where |a+bi|=1 .... I wil lbe able to fing a pattern?

8. ## Re: Roots of complex numbers

Originally Posted by Hyunqul
so if I started with adding the roots of an equation of Z^n=a+bi , where |a+bi|=1 .... I wil lbe able to fing a pattern?
No comment. Sorry

9. ## Re: Roots of complex numbers

aha ... but do you mean with "no comment" taht there is no known pattern for this ... or you want me to show my work I done first ?

10. ## Re: Roots of complex numbers

Originally Posted by Hyunqul
aha ... but do you mean with "no comment" taht there is no known pattern for this ... or you want me to show my work I done first ?

11. ## Re: Roots of complex numbers

Originally Posted by Hyunqul
Hello,

I need to find the relationship bewteen the power (n) in the equation : Z^n = a+bi , where |a+bi|=1 ...is it possible ? (Something other than De Moiver's theorem).

Thanks.