If `|z_1+z_2|> |z_1-z_2` then prove that `-pi/2 < arg (z_1/z_2)< pi/2.`

If |z_(1)+z_(2)|>|z_(1)-z_(2) then prove that -(pi)/(2)

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

if |z_1+z_2|=|z_1|+|z_2|, then prove that a r g(z_1)=a r g(z_2) if |z_1-z_2|=|z_1|+|z_2|, then prove that a r g(z_1)=a r g(z_2)=pi

If z_1 and z_2 be two non-zero complex numbers such that |z_1+z_2|=|z_1|+|z_2| ,then prove that argz_1-argz_2=0 .

if |z_(1)+z_(2)|=|z_(1)|+|z_(2)|, then prove that arg(z_(1))=arg(z_(2)) if |z_(1)-z_(2)|=|z_(1)|+|z_(2)| then prove that arg (z_(1))=arg(z_(2))=pi

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

If |z_1|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

If |z_1|=1,|z_2|=1 then prove that |z_1+z_2|^2+|z_1-z_2|^2 =4.

Given that |z_1+z_2|^2=|z_1|^2+|z_2|^2 , prove that z_1/z_2 is purely imaginary.

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