Find the locus of point `z` if `z ,i ,a n di z ,` are collinear.

If z_1, z_2, z_3 are three nonzero complex numbers such that z_3=(1-lambda)z_1+lambdaz_2w h e r elambda in R-{0}, then prove that points corresponding to z_1, z_2a n dz_3 are collinear .

Find the locus of a point, the sum of squares of whose distance from the planes x-z=0,x-2y+z=0a n dx+y+z=0i s36 .

Find the locus of z if |3z - 5 | = 3 |z + 1| where z = x + iy

Find the locus of a point, the sum of squares of whose distance from the planes x-z=0,x-2y+z=0 and x+y+z=0 is 36

Find the locus of the points representing the complex number z for which |z+5|^2-|z-5|^2=10.

Find the locus of z if Re ((z + 1)/(z-i)) = 0 where z = x + iy

Find the locus of z if Re ((bar(z) + 1)/(bar(z) - i)) = 0.

If z= x+iy find the locus of z if |2z+1| = 2 .

If |z-1|=2 then the locus of z is

If n >1 , show that the roots of the equation z^n=(z+1)^n are collinear.