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

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, 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 on a circle passing through the origin.

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.

Let z_(1)" and "z_(2) be the roots of the equation z^(2)+pz+q=0 , where p,q are real. The points represented by z_(1),z_(2) and the origin form an equilateral triangle if

If the imaginary part of (2z + 1)/(iz + 1) is -2 , then show that the locus of the point representing z in the argand plane is straight line.

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 (a) x/5=(y-1)/8=(z-2)/(-13) (b) x/2=(y-1)/3=(z-2)/(-5) (c) x/4=(y-1)/3=(z-2)/(-7) (d) x/2=(y-1)/(-7)=(z-2)/5

If |z/| barz |- barz |=1+|z|, then prove that z is a purely imaginary number.

Equation of the plane containing the straight line x/2=y/3=z/4 and perpendicular to the plane containing the straight lines x/2=y/4=z/2 and x/4=y/2=z/3 is

If |z|=1 and z ne +-1 , then one of the possible value of arg(z)-arg(z+1)-arg(z-1) , is

If |z|=1a n dz!=+-1, then all the values of z/(1-z^2) lie on (a)a line not passing through the origin (b) |z|=sqrt(2) (c)the x-axis (d) the y-axis