If `z=x+i ya n dw=(1-i z)//(z-i)` , then show that `|w|=1 z` is purely real.

If z=x+iy and w=(1-iz)/(z-i) , then |w|=1 implies that in the complex plane (A) z lies on imaginary axis (B) z lies on real axis (C) z lies on unit circle (D) None of these

Prove that z=i^i, where i=sqrt-1, is purely real.

If |(z-i)/(z+i)|=1 , then the locus of z is

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

If z = x + iy is a complex number such that |(z-4i)/(z+ 4i)| = 1 show that the locus of z is real axis.

If (1 + z)/(1 - z) = cos 2theta + i sin 2theta , show that z = i tan theta .

If z = (1)/((2 + 3i)^(2)) then |z| =

Let z_1z_2, z_3 z_n be the complex numbers such that |z_1|=|z_2||z_n|=1. If z=(sum_(k=1)^n z_k)(sum_(k=1)^n1/(z_k)) then proves that z is a real number

If z=((1+i)/(1-i))^(9) find z+(1)/(z)

If z=i^(i^(i)) where i=sqrt-1 then |z| is equal to