If `|z| <= 1 and |omega| <= 1,` show that `|z-omega|^2 <= (|z|-|omega|)^2+(arg z-arg omega)^2`

If |2z-1|=|z-2| and z_(1),z_(2),z_(3) are complex numbers such that |z_(1)-alpha| |z|d.>2|z|

If |2z-1|=|z-2| and z_1, z_2, z_3 are complex numbrs such that |z_1-alpha|ltalpha, |z_2-beta|ltbeta. Then (z_1+z_2)/(alpha+beta)|= (A) lt|z| (B) lt2|z| (C) gt|z| (D) gt2|z|

If | z_ (1) + z_ (2) | = | z_ (1) -z_ (2) |, then arg z_ (1) -arg z_ (2) =

Modulus of a Complex Number & its properties If z;z_1;z_2inCC then (i)|z|=0hArrz=0 i.e. Re(z)=Im(z)=0 (ii)|z|=|barz|=|-z| (iii) -|z|leRe(z)le|z|;-|z|leIm(z)le|z| (iv) zbarz=|z|^2 (v)|z_1z_2|=|z_1||z_2| (vi)|(z_1)/(z_2)|=|z_1|/|z_2|; z_2!=0