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Thread: graphic representaiton of |z-3| >= 2|z-4i|

  1. #1
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    graphic representaiton of |z-3| >= 2|z-4i|

    Hi everyone

    I need some help in seeing this complex exercice. The question is : "what does the following expression represent (graphic representation) : |z-3| >= 2|z-4i| ?"
    I tried to resolve this thing and this is how i begin

    |z-3| >= 2|z-4i|

    with z = (x+yi)

    => |(x+yi-3)|>= 2|(x+yi-4i)|
    => [(x+(yi)-(3)]^1/2 >= [2 (x+(y-4)]^1/2


    Is the begining right ?
    Someone can help me ?
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  2. #2
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    Re: graphic representaiton of |z-3| >= 2|z-4i|

    Quote Originally Posted by Nohrvald View Post
    I need some help in seeing this complex exercice. The question is : "what does the following expression represent (graphic representation) : |z-3| >= 2|z-4i| ?" I tried to resolve this thing and this is how i begin
    |z-3| >= 2|z-4i| with z = (x+yi)
    So $\displaystyle {(x - 3)^2} + {y^2} \ge 4\left[ {{x^2} + {{\left( {y - 4} \right)}^2}} \right]$
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  3. #3
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    Re: graphic representaiton of |z-3| >= 2|z-4i|

    thanks

    I found :

    -6x >= 3x + 3y - 32y + 55

    Honestly I don't know how to react with this expression :S
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  4. #4
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    Re: graphic representaiton of |z-3| >= 2|z-4i|

    complete the square and write

    $\displaystyle (x+1)^2+\left(y-\frac{16}{3}\right)^2\leq \text{ }\left(\frac{10}{3}\right)^2$
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  5. #5
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    Re: graphic representaiton of |z-3| >= 2|z-4i|

    Thank you for your aswer but i don't understand it

    Could you develop ?
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