Let `z_1 epsilon A and z_2 epsilon B` then the value of `|z_1-z_2|` necessarily lies between (A) 3 and 15 (B) 0 and 22 (C) 2 and 22 (D) 4 and 14

If z_1 and z_2 lies on |z|=9 and |z-3-4i|=4 respectively, find minimum possible value of |z_1 -z_2| (A) 0 (B) 5 (C) 13 (D) 2

If z_1 and z_2 are complex numbers such that |z_1-z_2|=|z_1+z_2| and A and B re the points representing z_1 and z_2 then the orthocentre of /_\OAB, where O is the origin is (A) (z_1+z_2)/2 (B) 0 (C) (z_1-z_2)/2 (D) none of these

for any complex nuber z maximum value of |z|-|z-1| is (A) 0 (B) 1/2 (C) 1 (D) 3/2

If z_1 , lies in |z-3|<=4,z_2 on |z-1|+|z+1|=3 and A = |z_1-z_2| , then :

If B: {z: |z-3-4i|}=5 and C={z:Re[(3+4i)z]=0} then the number of elements in the set B intesection C is (A) 0 (B) 1 (C) 2 (D) none of these

If z^3+(3+2i)z+(-1+i a)=0 has one real roots, then the value of a lies in the interval (a in R) (-2,1) b. (-1,0) c. (0,1) d. (-2,3)

If |z|= maximum {|z+2|,|z-2|} , then (A) |z- barz | = 1/2 (B) |z+ barz |=4 (C) |z+ barz |= 1/2 (D) | z-barz =2

If a=z_1+z_2+z_3, b=z_1+omega z_2+omega^2z_3,c=z_1+omega^2z_2+omegaz_3(1,omega, omega^2 are cube roots of unity), then the value of z_2 in terms of a,b, and c is (A) (aomega^2+bomega+c)/3 (B) (aomega^2+bomega^2+c)/3 (C) (a+b+c)/3 (D) (a+bomega^2+comega)/3

Show that for z epsilon C, |\z|=0 if and only if z=0

The points A(z_1), B(z_2) and C(z_3) form an isosceles triangle in the Argand plane right angled at B, then (z_1-z_2)/(z_3-z_2) can be (A) 1 (B) -1 (C) -i (D) none of these