Which of the following is correct for any two complex numbers `z_(1) " and" z_(2)` ?

Which of the following is correct for any tow complex numbers z_1a n dz_2? |z_1z_2|=|z_1||z_2| (b) a r g(z_1z_2)=a r g(z_1)a r g(z_2) (c) |z_1+z_2|=|z_1|+|z_2| (d) |z_1+z_2|geq|z_1|+|z_2|

Which of the following is correct for any tow complex numbers z_1a n dz_2? (a) |z_1z_2|=|z_1||z_2| (b) a r g(z_1z_2)=a r g(z_1)a r g(z_2) (c) |z_1+z_2|=|z_1|+|z_2| (d) |z_1+z_2|geq|z_1|+|z_2|

State true or false for the following. Let z_(1) " and " z_(2) be two complex numbers such that |z_(2) + z_(2)| = |z_(1) | + |z_(2)| , then arg (z_(1) - z_(2)) = 0

Statement-1: for any two complex numbers z_(1) and z_(2) |z_(1)+z_(2)|^(2) le (1+1/lamba)|z_(2)|^(2) , where lambda is a positive real number. Statement:2 AM ge GM .

If the triangle fromed by complex numbers z_(1), z_(2) and z_(3) is equilateral then prove that (z_(2) + z_(3) -2z_(1))/(z_(3) - z_(2)) is purely imaginary number

State true or false for the following. For any complex number z, the minimum value of |z| + |z-1| is 1 .

z_1a n dz_2 are two complex numbers satisfying i|z_1|^2z_2-|z_2|^2z_1=z_1-i z_2dot Then which of the following is/are correct? R e((z_1)/(z_2))=0 (b) I m((z_1)/(z_2))=0 z_1( z )_2+( z )_1z_2=0 (d) |z_1||z_2|=1or|z_1|=|z_2|

If z is any complex number, then the area of the triangle formed by the complex number z, wz and z+wz as its sides, is

For any complex number z, maximum value of |z|-|z-1| is

Statement -1 : For any four complex numbers z_(1),z_(2),z_(3) and z_(4) , it is given that the four points are concyclic, then |z_(1)| = |z_(2)| = |z_(3)|=|z_(4)| Statement -2 : Modulus of a complex number represents the distance form origin.