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_1ne-z_2 and |z_1+z_2|=|1/z_1 + 1/z_2| then :

If z_1 and z_2 are two complex numbers for which |(z_1-z_2)(1-z_1z_2)|=1 and |z_2|!=1 then (A) |z_2|=2 (B) |z_1|=1 (C) z_1=e^(itheta) (D) z_2=e^(itheta)

Which of the following are correct for any two complex numbers z_1 and z_2? (A) |z_1z_2|=|z_1||z_2| (B) arg(|z_1 z_2|)=(argz_1)(arg,z_2) (C) |z_1+z_2|=|z_1|+|z_2| (D) |z_1-z_2|ge|z_1|-|z_2|

If kgt1,|z_1|,k and |(k-z_1barz_2)/(z_1-kz_2)|=1 , then (A) z_2=0 (B) |z_2|=1 (C) |z_2|=4 (D) |z_2|ltk

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_1-1|=Re(z_1),|z_2-1|=Re(z_2) and arg (z_1-z_2)=pi/3, then Im (z_1+z_2) =

If |z_1+z_2| = |z_1-z_2| , prove that amp z_1 - amp z_2 = pi/2 .

If Z_(1)=1+i and Z_(2)=2+2i , then which of the following is not true. (A) |z_(1)z_(2)|=|z_(1)||z_(2)| (B) |z_(1)+z_(2)|=|z_(1)|+|z_(2)| (C) |z_(1)-z_(2)|=|z_(1)|-|z_(2)| (D) |(z_(1))/(z_(2))|=(|z_(1)|)/(|z_(2)|)

If z_1,z_2,z_3 be the vertices A,B,C respectively of triangle ABC such that |z_1|=|z_2|=|z_3| and |z_1+z_2|=|z_1-z_2| then C= (A) pi/2 (B) pi/3 (C) pi/6 (D) pi/4