If `|z^2 -1| = zbar(z)+1`, then show that z lies on the imaginary axis.

If iz^3+z^2-z+i = 0 , then show that |z|=1.

If |z^2-1|=|z|^2+1 , then z lies on :

If |z-iRe(z)|=|z-Im(z)|, then prove that z lies on the bisectors of the quadrants, " where "i=sqrt(-1).

If w= z/(z-i1/3) and |w|=1,then z lies on:

Prove that : z= -bar(z) iff z is either zero or purely imaginary.

If |z|=1 and z!=1, then all the values of z/(1-z^2) lie on

If |z|=1, prove that (z-1)/(z+1) (z ne -1) is purely imaginary number. What will you conclude if z=1?

If z_1,z_2 are comples numbers such that (2 z_1)/(3z_2) is purely imaginary number, then find |(z_1-z_2)/ (z_1+ z_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.

If |z-1|=1, where z is a point on the argand plane, show that (z-2)/(z)=i tan (argz),where i=sqrt(-1).