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Math Help - Unit circle help

  1. #1
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    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...
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  2. #2
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    Quote Originally Posted by domenfrandolic View Post
    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?
     z = a + bi\, \Rightarrow \,\left| z \right| = \sqrt {a^2  + b^2 }
    If |z|>1 then any root is exterior to the unit circle and interior if
    |z|<1

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