`|z|<=1,|w|<=1`, then show that `|z- w|^2<=(|z|-|w|)^2+(argz-argw)^2`

All complex numbers 'z' which satisfy the relation |z-|z+1||=|z+|z-1|| on the complex plane lie on the

If z_1, z_2, z_3, z_4 are the affixes of four point in the Argand plane, z is the affix of a point such that |z-z_1|=|z-z_2|=|z-z_3|=|z-z_4| , then z_1, z_2, z_3, z_4 are

Let z_(1),z_(2) and z_(3) be complex numbers such that |z_(1)|=|z_(2)|=|z_(3)|=1 then prove that |z_(1)+z_(2)+z_(3)|=|z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)|

If |z_1|=|z_2|=|z_3|"…."=|z_n|=1 then |z_(1)+z_(2)+"….."+z_(n)|=

If |z-z_(1)|=|z-z_(2)| then the locus of z is :

Let z_1 and z_2 be two distinct complex numbers and let z=(1-t)z_1+t z_2 for some real number t with 0 (a) |z-z_1|+|z-z_2|=|z_1-z_2| (b) arg(z-z_1)=arg(z-z_2) (c) (z-z_1) bar(z_2-z_1) = bar (z-z_1)(z_2-z_1) (d) a r g(z-z_1)=a r g(z_2-z_1) .

For any two complex numbers z_1 and z_2 , prove that |z_1+z_2| =|z_1|-|z_2| and |z_1-z_2|>=|z_1|-|z_2|

If |z_(1)+ z_(2)|=|z_(1)|+|z_(2)| , then arg z_(1) - arg z_(2) is