# Roots of complex numbers

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• Sep 27th 2011, 05:33 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, 06:26 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, 07:11 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, 07:27 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, $\displaystyle \frac{2\pi}{n}$.
• Sep 27th 2011, 12:04 PM
Hyunqul
Re: Roots of complex numbers
and there's no other mathematical relationship or pattern between them?
• Sep 27th 2011, 12:08 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?

Start with looking at the sum of the roots.
• Sep 27th 2011, 07:52 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, 08:06 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
Do you know anything about this topic?
If so, please tell us what you know, in detail, so we can truly help you.
• Sep 28th 2011, 05:47 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, 10:55 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 ?

Start thinking about the help you've been given and doing something instead of just fishing for more help.
• Sep 30th 2011, 03:36 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.

Asked here: http://www.mathhelpforum.com/math-he...de-187045.html

Thread closed.