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_1=a+ib and z_2=c+id are complex numbes such that |z_1|=|z_2|=1 and Re(z_1barz_2)=0 then the pair of complex numbers omega_1= a+ic and omega_2=b+id satisfy which of the following relations? (A) |omega_1|=1 (B) |omega_2|=1 (C) Re(omega_1 baromega_2)=0 (D) Im(omega_1baromega_2)=0

If (1)/(b+c),1/(c+a),1/(a+b) are are in HP, then which of the following is/are correct? 1 a, b, care in AP 2. (b+c)^2 (c + a)^2, (a + b)^2 are in GP

Show that the equation of the circle in the complex plane with z_1 & z_2 as its diameter can be expressed as , 2z barz-(barz_1+barz_2)z-(barz_1+barz_2)barz+z_1barz_2+z_2barz_1=0

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

Let A(z_1), B(z_2) and C(z_3) forms an acute angled triangle in argand plane having origin as it’s orthocentre. Prove that z_1barz_2+bar(z)_1 z_2=z_2barz_3+barz_2z_3=z_3barz_1 +barz_3z_1

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

Solve: z +2barz=ibarz

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