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

1. ## 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)|
=> [(x²+(yi)²-(3)²]^1/2 >= [2 (x²+(y-4)²]^1/2

Is the begining right ?
Someone can help me ?

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

Originally Posted by Nohrvald
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 $\displaystyle {(x - 3)^2} + {y^2} \ge 4\left[ {{x^2} + {{\left( {y - 4} \right)}^2}} \right]$

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

thanks

I found :

-6x >= 3x² + 3y² - 32y + 55

Honestly I don't know how to react with this expression :S

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

complete the square and write

$\displaystyle (x+1)^2+\left(y-\frac{16}{3}\right)^2\leq \text{ }\left(\frac{10}{3}\right)^2$

5. ## Re: graphic representaiton of |z-3| >= 2|z-4i|

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

Could you develop ?