Which of the following is (are) correct? (A) `barz_1+abarz_2=2b` (B) `barz_1+abarz_2=b` (C) `barz_1+abarz_2=-b` (D) `barz_1+abarz_2=-2b`

Which of the following is (are) correct? (A) bara z_1+abarz_1-baraz_2-abarz_2=0 (B) bara z_1+abarz_1+baraz_2+abarz_2=-b (C) bara z_1+abarz_1+baraz_2+abarz_2=2b (D) bara z_1+abarz_1+baraz_2+abarz_2=-2b

Which of the following is (are) correct? (A) bar(z_1-z_2)-a(barz_1-barz_2)=0 (B) bar(z_1-z_2)+a(barz_1-barz_2)=0 (C) bar(z_1-z_2)+a(barz_1-barz_2)=-b (D) bar(z_1-z_2)+a(barz_1-barz_2)=-b

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 z_(1) = 3+ 2i and z_(2) = 2-i then verify that (i) bar(z_(1) + z_(2)) = barz_(1) + barz_(2)

If z_1 and z_2 are two complex numbers such that |(barz_1-2barz_2)(2-z_1barz_2)|=1 then (A) |z_1|=1, if |z_2|!=1 (B) |z_1|=2, if |z_2|!=1 (C) |z_2|=2, if |z_1|!=1 (D) |z_2|=1, if |z_1|!=2

Prove that equation of perpendicular bisector of line segment joining complex numbers z_(1) and z_(2) is z(barz_(2) - barz_(1)) + barz (z_(2) + z_(1)) + |z_(1)|^(2) -|z_(2)|^(2) =0

For two unimodular complex number z_1a n dz_2 [[barz_1, -z_2], [barz_2, z_1]]^(-1) [[(z_1, z_2], [-barz_2, barz_1]]^(-1) is equal to [(z_1, z_2), (z_1bar, z_2bar)]^ b. [1 0 0 1] c. [1//2 0 0 1//2] d. none of these

Show that the triangle whose vertices are z_1,z_2,z_3 and barz_1, barz_2 and barz_3 and z_1\',z_2\',z_3\' are similar if |(z_1,z_1\',1),(z_2,z_2\', 1),(z_3, z_3\' 1)|=0 or z_1(z_2\'-z_3\')+z_2(z_3\'-z_1\')+(z_1\'-z_2\')=0

if z=3 -2i, then verify that (i) z + barz = 2Rez (ii) z - barz = 2ilm z

Find the complex number z if zbarz = 2 and z + barz=2