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

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

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

ReplyDeletewhat you calculated is the length of the line connecting A with the point (-2,0).

ReplyDeletedid 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

how to check?

ReplyDeletefor example by taking your value of z?

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

ReplyDeletein 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