" If "|z|<=4" then find the maximurn value of "|iz+3-4i|

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

If |z_(1)|=|z_(2)|=|z_(3)| and z_(1)+z_(2)+z_(3)=0 , then z_(1),z_(2),z_(3) are vertices of

If |z_(1)|=1,|z_(2)|=2,|z_(3)|=3 ,then |z_(1)+z_(2)+z_(3)|^(2)+|-z_(1)+z_(2)+z_(3)|^(2)+|z_(1)-z_(2)+z_(3)|^(2)+|z_(1)+z_(2)-z_(3)|^(2) is equal to

, a point 'z' is equidistant from three distinct points z_(1),z_(2) and z_(3) in the Argand plane. If z,z_(1) and z_(2) are collinear, then arg (z(z_(3)-z_(1))/(z_(3)-z_(2))). Will be (z_(1),z_(2),z_(3)) are in anticlockwise sense).

If |z_1|=|z_2|=.......=|z_n|=1, prove that |z_1+z_2+z_3++z_n|=1/(z_1)+1/(z_2)+1/(z_3)++1/(z_n)

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

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))|

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