If (z-1)/(z+1) is purely imaginary then

If z is a complex number such that (z-1)/(z+1) is purely imaginary, then the value of |z| is-

If z=x+iyand(z-i)/(z+1) is purely imaginary, then show that the point z always lies on a circle.

If z=x+iy and (z-i)/(z+1) is purely imaginary,then show that the point z always lies on a circle.

Let z=x+iy , where x and y are real. The points (x,y) in the xy-plane of which (z+1)/(z-1) is purely imaginary, lie on

If z be complex no. and (z-1)/(z+1) be purely imaginary show that z lies on the circle whose centre is at origin and the radius is 1

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

If z_1, z_2 are two complex numbers (z_1!=z_2) satisfying |z_1^2-z_2^2|=| z_ 1^2+ z _2 ^2-2( z _1)( z _2)| , then a. (z_1)/(z_2) is purely imaginary b. (z_1)/(z_2) is purely real c. |a r g z_1-a rgz_2|=pi d. |a r g z_1-a rgz_2|=pi/2

If z=x+iy and |z|=1 , show that (z-1)/(z+1)(z!=-1) is a purely imaginary quantity.

P(z_1),Q(z_2),R(z_3)a n dS(z_4) are four complex numbers representing the vertices of a rhombus taken in order on the complex lane, then which one of the following is/ are correct? (z_1-z_4)/(z_2-z_3) is purely real a m p(z_1-z_4)/(z_2-z_3)=a m p(z_2-z_4)/(z_3-z_4) (z_1-z_3)/(z_2-z_4) is purely imaginary It is not necessary that |z_1-z_3|!=|z_2-z_4|

Let (z-alpha)/(z+alpha) is purely imaginary and |z|=2, alphaepsilonR then alpha is equal to (A) 2 (B) 1 (C) sqrt2 (D) sqrt3