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Finding value in a complex set region

  1. Apr 21, 2015 #1
    1. The problem statement, all variables and given/known data

    The largest value of r for which the region represented by the set { ω ε C / |ω - 4 - i| ≤ r}
    is contained in the region represented by the set { z ε C / |z - 1| ≤ |z + i|}, is equal to :
    √17
    2√2
    3/2 √2
    5/2 √2
    2. Relevant equations
    complex number = a + ib where a,b ε R

    3. The attempt at a solution
    Don't know how to start or what to apply
     
  2. jcsd
  3. Apr 21, 2015 #2
    Hi!!!
    Hint: the set |w-4-i| ≤r represents the region inside the circle with its centre (4, 1) and radius r.
     
  4. Apr 21, 2015 #3
    Hello Mooncrater
    Okay, we know centre of circle as (4,1) and radius r.
    Now taking z= x + iy,
    we get from question
    (x - 1)2 + y2 ≤ x2+ (y+1)2
    ⇒ -x ≤ y
    Now what?
     
  5. Apr 21, 2015 #4
    Now each equation(the circle and the line) points out where a point can be.. like a constraint.
     
  6. Apr 21, 2015 #5
    So should we differentiate to get max. Value of r?
    Is it a minima and maxima problem?
     
  7. Apr 21, 2015 #6
    You can do it through graph... it will be very easier then. I think maxima would work if you want it to do it that way...
     
  8. Apr 21, 2015 #7
    Is the D option 5√2/2 or 5/2√2?
     
  9. Apr 21, 2015 #8
    What's the line equation?
    Is it y = -x ?
    And circle equation is (x-4)2 + (y-1)2 = r2 ?
    The D option is 5√2/2 .
     
  10. Apr 21, 2015 #9
    Yes.
     
  11. Apr 22, 2015 #10
    Got it, thanks the D option.
     
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