If`|z|=1` , then prove that points represented by `sqrt((1+z)//(1-z))` lie on one or other of two fixed perpendicular straight lines.

if |z|=3 then the points representing thecomplex numbers -1+4z lie on a

If |z|=1, then the point representing the complex number -1+3z will lie on a. a circle b. a parabola c. a straight line d. a hyperbola

If z_1^2+z_2^2-2z_1.z_2.costheta= 0 prove that the points represented by z_1, z_2 , and the origin form an isosceles triangle.

If z_1, z_2, z_3 are complex numbers such that (2//z_1)=(1//z_2)+(1//z_3), then show that the points represented by z_1, z_2()_, z_3 lie one a circle passing through e origin.

If z_1, z_2, z_3 are complex numbers such that (2//z_1)=(1//z_2)+(1//z_3), then show that the points represented by z_1, z_2, z_3 lie one a circle passing through the origin.

Perpendicular are drawn from points on the line (x+2)/(2)=(y+1)/(-1)=(z)/(3) to the plane x+y+z=3 . The feet of perpendiculars lie on the line.

If |z|=2, the points representing the complex numbers -1+5z will lie on

If |z|=2, the points representing the complex numbers -1+5z will lie on

If z ne 1 and (z^(2))/(z-1) is real, then the point represented by the complex number z lies

Perpendiculars are drawn from points on the line (x+2)/2=(y+1)/(-1)=z/3 to the plane x + y + z=3 The feet of perpendiculars lie on the line