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 omega = z//[z-(1//3)i] and |omega| = 1 , then find the locus of z.

If z is any complex number, prove that : |z|^2= |z^2| .

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 :

If Z is a complex number, then |Z-8| lt= |Z-2|implies:

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 :

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

For any two complex numbers z_1 and z_2 , prove that Re (z_1 z_2) = Re z_1 Re z_2 - Imz_1 Imz_2

Let z be a complex number such that the imaginary part of z is nonzero and a = z^(2) + z+z+1 is real. Then a cannot take the value.

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