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) 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) 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

Which of the following is correct for any tow complex numbers z_1a n dz_2? |z_1z_2|=|z_1||z_2| (b) a r g(z_1z_2)=a r g(z_1)a r g(z_2) (c) |z_1+z_2|=|z_1|+|z_2| (d) |z_1+z_2|geq|z_1|+|z_2|

Which of the following is correct for any tow complex numbers z_1a n dz_2? (a) |z_1z_2|=|z_1||z_2| (b) a r g(z_1z_2)=a r g(z_1)a r g(z_2) (c) |z_1+z_2|=|z_1|+|z_2| (d) |z_1+z_2|geq|z_1|+|z_2|

Prove that the circles z bar z +z( bar a _1)+bar z( a_1 )+b_1=0 ,b_1 in R and z bar z +z( bar a _2)+ bar z a_2+b_2=0, b_2 in R will intersect orthogonally if 2R e(a_1 bar a _2)=b_1+b_2dot

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 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

If z_1 and z_2 two non zero complex numbers such that |z_1+z_2|=|z_1| then which of the following may be true (A) argz_1-argz_2=0 (B) argz_1-argz_2=pi (C) |z_1-z_2|=||z_1|-|z_2|| (D) argz_1-argz_2=4pi

If |z_1/z_2|=1 and arg (z_1z_2)=0 , then a. z_1 = z_2 b. |z_2|^2 = z_1*z_2 c. z_1*z_2 = 1 d. none of these

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