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Math Help - Defining a unit circle.

  1. #1
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    Defining a unit circle.

    Here's an easy one for someone.

    How do I define a unit circle in the complex plane that's not centred at the origin, specifically I need to define one centred at  2 \pi and one centred at  2 \pi i .
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  2. #2
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    Re: Defining a unit circle.

    Hey rushton.

    The circle in complex numbers is defined by |z| = R. But if you shift z by some constant, how will that affect where the circle is?

    Hint: Recall that in normal real number math, (x-a)^2 + (y-b)^2 = R^2 is centred at (a,b) with a radius of R.
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  3. #3
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    Re: Defining a unit circle.

    Quote Originally Posted by rushton View Post
    How do I define a unit circle in the complex plane that's not centred at the origin, specifically I need to define one centred at  2 \pi and one centred at  2 \pi i .
    Recall that for complex numbers z~\&~w the |z-w| is the distance between them.

    Informally we can write |z-2\pi|=1~\&~|z-2\pi i|=1.

    More formally \{z:~|z-2\pi i|=1\}, the set of numbers a distance of 1 from 2\pi i.
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