If z and `omega` are two complex numbers such that `|zomega| =1 and arg(z)-arg(omega)=pi/2`, then prove that `bar(z)omega=-i`

If z and w are two non-zero complex numbers such that |zw|=1 and Arg (z) -Arg (w) =pi/2 , then bar z w is equal to :

Let z and w be two non-zero complex numbers such that ∣z∣=∣w∣ and arg(z)+arg(w)=π, then z equals

The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

Let z and w are two non zero complex number such that |z|=|w|, and Arg(z)+Arg(w)=pi then (a) z=w (b) z=overlinew (c) overlinez=overlinew (d) overlinez=-overlinew

Let z and w be two complex numbers such that |z|le1, |w|le1 and |z-iw|=|z-i bar w|=2 , then z equals :

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

Let z and omega be complex numbers. If Re(z) = |z-2| , Re(omega) = |omega - z| and arg(z - omega) = pi/3 , then the value of Im(z+w) , is

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

If z_1=a + ib and z_2 = c + id are complex numbers such that |z_1|=|z_2|=1 and Re(z_1 bar z_2)=0 , then the pair of complex numbers omega_1=a+ic and omega_2=b+id satisfies a. |omega_(1)|=1 b. |omega_(2)|=1 c. Re(omega_(1)baromega_(2))=0 d. None of these

If z_1 and z_2 (ne 0) are two complex numbers, prove that : |z_1 z_2|= |z_1||z_2| .