If `z` lies on the curve `a r g(z+1)=pi/4` , then the minimum value of `|z-omega|+|z+omega|,w h e romega=e^(i(2pi)/3)` , is

If z satisfies the condition arg (z + i) = (pi)/(4) . Then the minimum value of |z + 1 - i| + |z - 2 + 3 i| is _______.

If complex number z lies on the curve |z - (- 1+ i)| = 1 , then find the locus of the complex number w =(z+i)/(1-i), i =sqrt-1 .

Find the locus of z if omega= (z)/(z- (1)/(3)i), |omega| =1

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

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

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

Let z and omega be two non zero complex numbers such that |z|=|omega| and argz+argomega=pi , then z equals (A) omega (B) -omega (C) baromega (D) -baromega

Let z and omega be two non zero complex numbers such that |z|=|omega| and argz+argomega=pi, then z equals (A) omega (B) -omega (C) baromega (D) -baromega

Complex number z lies on the curve S-= arg(z+3)/(z+3i) =-(pi)/(4)

If a=z_1+z_2+z_3, b=z_1+omega z_2+omega^2z_3,c=z_1+omega^2z_2+omegaz_3(1,omega, omega^2 are cube roots of unity), then the value of z_2 in terms of a,b, and c is (A) (aomega^2+bomega+c)/3 (B) (aomega^2+bomega^2+c)/3 (C) (a+b+c)/3 (D) (a+bomega^2+comega)/3