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Math Help - complex numbers and sets

  1. #1
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    complex numbers and sets

    When given the sets X = { z is complex, mod(z) < 2}, Y = { z is complex, z - z* = 2i} where z* is the complex conjugate, draw these on an argand diagram.
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    Re: complex numbers and sets

    Quote Originally Posted by qwerty31 View Post
    When given the sets X = { z is complex, mod(z) < 2}, Y = { z is complex, z - z* = 2i} where z* is the complex conjugate, draw these on an argand diagram.
    Try writing \displaystyle \begin{align*} z = x + i\,y \end{align*} and see what "form" these relations then take.
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    Re: complex numbers and sets

    Quote Originally Posted by Prove It View Post
    Try writing \displaystyle \begin{align*} z = x + i\,y \end{align*} and see what "form" these relations then take.
    I got that the first one is a circle with radius 2 and under...for the second one I seem to get y = 1, and Im not too sure about that
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    Re: complex numbers and sets

    Quote Originally Posted by qwerty31 View Post
    I got that the first one is a circle with radius 2 and under...for the second one I seem to get y = 1, and Im not too sure about that
    No, the first is not the circle with radius 2 and under, it's the circle with radius LESS than 2.

    The second is correct. So it's a horizontal line where y = 1 (or where Im(z) = 1).
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    Re: complex numbers and sets

    Quote Originally Posted by Prove It View Post
    No, the first is not the circle with radius 2 and under, it's the circle with radius LESS than 2.

    The second is correct. So it's a horizontal line where y = 1 (or where Im(z) = 1).
    Oh, I forgot to put the 'less than or equal to' sign for the first one, sorry about that! And thank you
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