# Roots of complex numbers

• Sep 27th 2011, 06:33 AM
Hyunqul
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.
• Sep 27th 2011, 07:26 AM
Plato
Re: Roots of complex numbers
Quote:

Originally Posted by Hyunqul
I need to find the relationship bewteen the power (n) and what?

You do not have a compete thought there.
• Sep 27th 2011, 08:11 AM
Hyunqul
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.
• Sep 27th 2011, 08:27 AM
Plato
Re: Roots of complex numbers
Quote:

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, $\frac{2\pi}{n}$.
• Sep 27th 2011, 01:04 PM
Hyunqul
Re: Roots of complex numbers
and there's no other mathematical relationship or pattern between them?
• Sep 27th 2011, 01:08 PM
Plato
Re: Roots of complex numbers
Quote:

Originally Posted by Hyunqul
and there's no other mathematical relationship or pattern between them?

Why don't you investigate that?

• Sep 27th 2011, 08:52 PM
Hyunqul
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?
• Sep 27th 2011, 09:06 PM
Plato
Re: Roots of complex numbers
Quote:

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
• Sep 28th 2011, 06:47 AM
Hyunqul
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 ?
• Sep 29th 2011, 11:55 PM
mr fantastic
Re: Roots of complex numbers
Quote:

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 ?

• Sep 30th 2011, 04:36 AM
mr fantastic
Re: Roots of complex numbers
Quote:

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.