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Math Help - Complex Numbers

  1. #1
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    Complex Numbers

    Describe the set of points in the complex plane that satisfy the given equation:

    |z-1|=1

    |z|+|-1|=1\Rightarrow \sqrt{x^2+y^2}+1=1\Rightarrow \sqrt{x^2+y^2}=0

    x^2+y^2=0

    The answer is supposed to be a circle centered at (1,0) with a radius of 1.

    What am I doing wrong?
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  2. #2
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    Quote Originally Posted by dwsmith View Post
    Describe the set of points in the complex plane that satisfy the given equation: |z-1|=1

    |z|+|-1|=1 THIS IS WRONG
    What am I doing wrong?
    |z-1|=1 means (x-1)^2+y^2=1.
    That is the circle with center (1,0) & radius 1.
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  3. #3
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    Quote Originally Posted by dwsmith View Post
    Describe the set of points in the complex plane that satisfy the given equation:

    |z-1|=1

    |z|+|-1|=1\Rightarrow \sqrt{x^2+y^2}+1=1\Rightarrow \sqrt{x^2+y^2}=0

    x^2+y^2=0

    The answer is supposed to be a circle centered at (1,0) with a radius of 1.

    What am I doing wrong?
    z=x+iy

    z-1=x-1+iy

    |z-1|=\sqrt{(x-1)^2+y^2}=1

    (x-1)^2+y^2=1
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