If `|z|=2` and locus of `5z-1` is the circle having radius a and `z_1^2+z_2^2-2z_1z_2 cos theta=0, then |z_1|:|z_2|=` (A) a (B) 2a (C) `a/10` (D) none of these

If |z|=2 and the locus of 5z-1 is the circle having radius 'a' and z_(1)^(2)+z_(2)^(2)-2z_(1)z_(2)cos theta=0 then |z_(1)|:|z_(2)|=

Prove that |z_1+z_2|^2+|z_1-z_2|^2 =2|z_1|^2+2|z_2|^2 .

The complex numbers z_1, z_2 and the origin form an equilateral triangle only if (A) z_1^2+z_2^2-z_1z_2=0 (B) z_1+z_2=z_1z_2 (C) z_1^2-z_2^2=z_1z_2 (D) none of these

If f(z)=(7-z)/(1-z^2) , where z=1+2i , then |f(z)| is (a)(|z|)/2 (b) |z| (c) 2|z| (d) none of these

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

If amp (z_(1)z_(2))=0 and |z_(1)|=|z_(2)|=1, then z_(1)+z_(2)=0 b.z_(1)z_(2)=1 c.z_(1)=z_(2)^(*) d.none of these

If |z_1+z_2|=|z_1-z_2| and |z_1|=|z_2|, then (A) z_1=+-iz_2 (B) z_1=z_2 (C) z_=-z_2 (D) z_2=+-iz_1

If z_1 , z_2 are nonreal complex and |(z_1+z_2)/(z_1-z_2)| =1 then (z_1)/(z_2) is

Prove that |1-barz_1z_2|^2-|z_1-z_2|^2=(1-|z_1|^2)(1-|z_2|^2) .