If `abs(z) le 1` and `abs(omega) le 1`, show that
`abs(z-omega)^(2) le (abs(z)-abs(omega)^(2))+{arg(z)-arg(omega)}^(2)`.

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

If 1, omega, omega^(2) are three cube roots of unity, show that (a + omega b+ omega^(2)c) (a + omega^(2)b+ omega c)= a^(2) + b^(2) + c^(2)- ab- bc - ca

If |z|=k and omega=(z-k)/(z+k) , then Re (omega) =

If abs(z+4) le 3 , the maximum value of abs(z+1) is

Numbers of complex numbers z, such that abs(z)=1 and abs((z)/bar(z)+bar(z)/(z))=1 is

If z=x + yi and omega= (1-zi)/(z-i) show that |omega|=1 rArr z is purely real

If z and omega are two non-zero complex numbers such that |zomega|=1 and arg(z)-arg(omega)=pi/2 , then barzomega is equal to

Statement-1, if z_(1) and z_(2) are two complex numbers such that |z_(1)| le 1, |z_(2)| le 1 , then |z_(1)-z_(2)|^(2) le (|z_(1)|-|z_(2)|)^(2)-"arg"(z_(2))}^(2) Statement-2 sintheta gt theta for all theta gt 0 .

Let z and omega be complex numbers such that |z|=|omega| and arg (z) dentoe the principal of z. Statement-1: If argz+ arg omega=pi , then z=-baromega Statement -2: |z|=|omega| implies arg z-arg baromega=pi , then z=-baromega

Let z and omega be two non-zero complex numbers, such that |z|=|omega| and "arg"(z)+"arg"(omega)=pi . Then, z equals