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

If |z-4/z|=2 then the greatest value of |z| is

If |z_1|=|z_2|=|z_3|=|(1)/z_1+1/z_2+1/z_3|=1 then |z_1+z_2+z_3| = ...... .

If |z+1|=z+2(1+i) then find the value of z.

If |z-1|^(2)=|z|^(2)+1 then in the grand plane, z lines an.....

If z in z and |z+3| le 8 then find the maximum and minimum value of |z-2| .

If z_(1),z_(2)andz_(3) are the affixes of the vertices of a triangle having its circumcentre at the origin. If zis the affix of its orthocentre, prove that Z_(1)+Z_(2)+Z_(3)-Z=0.

State true of false for the following: If z is a complex number such that z ne0 and Re(z)=0 then 1_(m)(z^(2))=0

If |z_(1)|=|z_(2)|=....|z_(n)|=1 , then show that, |z_(1)+z_(2)+z_(3)+....z_(n)|= |(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))+...+(1)/(z_(n))|

The number of values of z (real or complex) e simultaneously satisfying the system of equations 1+z+z^2+z^3+...z^17=0 and 1+z+z^2+z^3+..+z^13=0 is