Let `z ne 1` be a complex number and let `omeg= x+iy, y ne 0`. If `(omega- bar(omega)z)/(1-z)` is purely real, then `|z|` is equal to

Let z be a complex number satisfying |z+16|=4|z+1| . Then

Let z and omega be two complex numbers such that |z|lt=1,|omega|lt=1 and |z-iomega|=|z-i bar omega|=2, then z equals (a) 1ori (b). ior-i (c). 1or-1 (d). ior-1

Let omega be a complex number such that 2omega+1=z where z=sqrt(-3.) If|1 1 1 1-omega^2-1omega^2 1omega^2omega^7|=3k , then k is equal to : -1 (2) 1 (3) -z (4) z

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

Let w ne pm 1 be a complex number. If |w|=1" and "z=(w-1)/(w+1) , then Re(z) is equal to

If omega=(z)/(z-(1/3)i)" and "|omega|=1 , then z lies on

Let z, omega be complex numbers such that bar(z)+ibar(omega)=0" and "arg z omega= pi . Then arg z equals

If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition that ((w- barw z)/(1-z)) is a purely real, then the set of values of z is |z|=1,z!=2 (b) |z|=1a n dz!=1 z= z (d) None of these

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