CIE 9709 Pure Maths Paper 3, May/June 2013 - question 9


4 comments:

  1. I think the greatest possible modulus of z was {(2^2 + 2^2)^0.5 + r(=2)}=4.83?

    ReplyDelete
  2. what you calculated is the length of the line connecting A with the point (-2,0).
    did you get the same shaded region? did you check if your z is satisfying both inequalities?
    z can be any point in the shaded region - magnitude of it is the length of the line connecting the point representing z to the origin

    ReplyDelete
  3. how to check?

    for example by taking your value of z?

    ReplyDelete
  4. the longest distance from origin to any point in the shaded region is representing the modulus of z

    in my case I can calculate the exact value of z to check the inequlities
    z=a+bi
    2a^2=4 ==> a=root(2)
    b=2+root(2)
    z= root(2)+ (2+root(2))i
    z-2i=root2 + root(2)i ==> |z-2i|=2
    z+2 = 2+root(2) +(2+root(2))i
    arg(z+2)=pi/4

    ReplyDelete