If `zinC` and |z| =1, then prove that `(z-1)/(z+1)` is either 0 or purely imaginary.

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

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=x+iy and |z|=1, show that the complex number z_1=(z-1)/(z+1) is purely imagine.

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

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

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)| .

If i z^4+1=0, then prove that z can take the value cospi//8+is inpi//8.

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

If a is a complex number such that |a|=1 , then find the value of a, so that equation az^2 + z +1=0 has one purely imaginary root.

If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition that ((w- bar w 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 (c) z=bar z (d) None of these