# Unit circle help

• May 17th 2011, 09:16 AM
domenfrandolic
Unit circle help
So we are given this complex number z=1+0i...we put it on the graph on in a unit circle and we see that is on the unit circle...what happens if the modulus of a complex number is > 1 or <1..?of course then the root of the complex number will be out or inside the unit circle.but how could i prove it or is there any way of stating it, any formula or whatever...
• May 17th 2011, 09:38 AM
Plato
Quote:

Originally Posted by domenfrandolic
So we are given this complex number z=1+0i...we put it on the graph on in a unit circle and we see that is on the unit circle...what happens if the modulus of a complex number is > 1 or <1..?of course then the root of the complex number will be out or inside the unit circle.but how could i prove it or is there any way of stating it, any formula or whatever...

Do you know how to find the modulus(absolute value) of a complex number?
$\displaystyle z = a + bi\, \Rightarrow \,\left| z \right| = \sqrt {a^2 + b^2 }$
If $\displaystyle |z|>1$ then any root is exterior to the unit circle and interior if
$\displaystyle |z|<1$

If fact, any $\displaystyle n^{th}$ root of $\displaystyle z$ is on a circle centered at the origin and radius $\displaystyle \sqrt[n]{{\left| z \right|}}$.