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 alpha=(z-i)(z+i), show that, when z lies above the real axis, alpha will lie within the unit circle which has center at the origin. Find the locus of alphaa sz travels on the real axis from -ooto+oodot

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

If z=x+i y and w=(1-i z)/(z-i) , show that |w|=1 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 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 z=x + yi and omega= (1-zi)/(z-i) show that |omega|=1 rArr z is purely real

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 z=x+i y and w=(1-i z)//(z-i) and |w| = 1 , then show that z is purely real.

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

If the ratio (z-i)/(z-1) is purely imaginary, prove that the point z lies on the circle whose centre is the point (1)/(2) (1+i) and radius is (1)/(sqrt2)