If `alpha = (z - i)//(z + i)` show that, when z lies above the real axis, `alpha`will lie within the unit circle which has centre at the origin. Find the locus of `alpha ` as z travels on the real axis form `-oo "to" + oo`

If |(z-5i)/(z+5i)|=1 show that z is a real number

All roots of the equation,(1+z)^(6)+z^(6)=0(A) lie on a unit circle with centre at the origin

If (z+i)/(z+2i) is purely real then find the locus of z

If Re ((z + 2i)/(z+4))= 0 then z lies on a circle with centre :

If z=x+iy and w=(1-iz)/(z-i), show that |w|=1o+_(z) is purely real.

If z!=1 and (z^2)/(z-1) is real, then the point represented by the complex number z lies (1) either on the real axis or on a circle passing through the origin (2) on a circle with centre at the origin (3) either on the real axis or on a circle not passing through the origin (4) on the imaginary axis

If the real part of (z+2)/(z-1) is 4, then show that the locus of he point representing z in the complex plane is a circle.

If the real part of (z+4)/(2z+i) is 1/2 then the point z lies on _______.

A disc is kept on xy plane with centre at origin. Find electric field at a point with distance Z from origin on z-axis.