If `|z_1+z_2|^2=|z_1|^2+|z_z|^2` then

For any two complex numbers z_1 and z_2 , we have |z_1+z_2|^2=|z_1|^2+|z_2|^2 , then

For any two complex numbers z_1 and z_2 , we have |z_1+z_2|^2=|z_1|^2+|z_2|^2 , then

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

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

Prove that |z_1+z_2|^2 = |z_1|^2 + |z_2|^2 if z_1/z_2 is purely imaginary.

If z_1, z_2 in C , then say which are true and false - . |z_1+z_2|^2=|z_1""|^2+|z_2|^2-2R e(z_1 z_2) |z_1-z_2|^2=|z_1""|^2-|z_2|^2-2R e(z_1 z_2) |z_1+z_2|^2+|z_1-z_2|^2=2(|z_1|^2+|z_2|^2) |a z_1-b z_2|^2+|b z_1+a z_2|^2=(a^2+b^2)(|z_1|^2+|z_2|^2) , where a ,b in Rdot

For any two complex numbers z_1 and z_2 prove that: |\z_1+z_2|^2=|\z_1|^2+|\z_2|^2+2Re bar z_1 z_2

If |z_1|le1,|z_2|le1"show that" |1-z_1z_2|^2-|z_1-z_2|^2=(1-|z_1|^2)(1-|z_2|^2 "Hence or otherwise show that." |(z_1-z_2)/(1-z_1z_2)|lt 1"if"|z_1| lt 1,|z_2| lt 1

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

Let z_1=r_1(costheta_1+isintheta_1)a n dz_2=r_2(costheta_2+isintheta_2) be two complex numbers. Then prove that |z_1+z_2|^2=r1 2+r2 2+2r_1r_2cos(theta_1-theta_2) or |z_1+z_2|^2=|z_1|^2+|z_2|^2+2|z_1||z_2|^()_cos(theta_1-theta_2) |z_1-z_2|^2=r1 2+r2 2-2r_1r_2cos(theta_1-theta_2) or |z_1-z_2|^2=|z_1|^2+|z_2|^2-2|z_1||z_2|^()_cos(theta_1-theta_2)