If `abs(z_1)` = `abs(z_2)`, is it necessary that `z_1`=`z_2` ?

If abs(z) = max{abs(z-2),abs(z+2)} , then

If abs(z+1) = z+2 (1+i), then find z

If abs(z^2-1) =(abs(z))^2+1 , then z lies on

If abs(z_1) = abs(z_2) = ........= abs(z_n) =1, then show that abs(z_1+ z_2+.......+z_n) = abs(frac{1}{z_1}+frac{1}{z_2}+.........frac{1}{z_n})

If abs(z_1+z_2) = abs(z_1-z_2) , then the difference in the amplitudes of z_1 and z_2 is

If z_1 and z_2 are two non-zero complex numbers such that abs(z_1+z_2) = abs(z_1)+abs(z_2) , then arg(z_1)-arg(z_2) is equal to

If z_1 = a+ib and z_2 = c+id are complex numbers such that abs(z_1) = abs(z_2) = 1 and Re(z_1barz_2) = 0 , then the pair of complex numbers w_1 = a+ic and w_2 = b+id satisfies

If abs(z_1)=abs(z_2)=….....=abs(z_n) = 1 then the value of abs(z_1+z_2+z_3+…....+z_n) =

If z_1, z_2, z_3 are complex numbers such that abs(z_1)= abs(z_2) = abs(z_3) = abs(frac{1}{z_1}+frac{1}{z_2}+frac{1}{z_3}) = 1 , then abs(z_1+z_2+z_3) is

Let z_1 and z_2 be two complex numbers such that z_1+z_2 and z_1z_2 both are real, theb