What is the locus of `w` if `w=3/za n d|z-1|=1?`

If |z|=1 and let omega=((1-z)^2)/(1-z^2) , then prove that the locus of omega is equivalent to |z-2|=|z+2|

What is locus of z if |z-1-sin^(-1)(1/sqrt3)|+|z+cos^(-1)(1/sqrt3)-pi/2|=1?

If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition that ((w- barw z)/(1-z)) is a purely real, then the set of values of z is |z|=1,z!=2 (b) |z|=1a n dz!=1 z= z (d) None of these

If the volume of tetrahedron A B C D is 1 cubic units, where A(0,1,2),B(-1,2,1)a n dC(1,2,1), then the locus of point D is a. x+y-z=3 b. y+z=6 c. y+z=0 d. y+z=-3

Let z=t^2-1+sqrt(t^4-t^2),w h e r et in R is a parameter. Find the locus of z depending upon t , and draw the lous of z in the Argand plane.

If omega is the complex cube root of unity then |[1,1+i+omega^2,omega^2],[1-i,-1,omega^2-1],[-i,-i+omega-1,-1]|=

If |z-1|=|z-3| then the locus of z is

Is W subset of N or Z?

if omegaa n domega^2 are the nonreal cube roots of unity and [1//(a+omega)]+[1//(b+omega)]+[1//(c+omega)]=2omega^2 and [1//(a+omega)^2]+[1//(b+omega)^2]+[1//(c+omega)^2]=2omega^ , then find the value of [1//(a+1)]+[1//(b+1)]+[1//(c+1)]dot

If z=z_0+A( bar z -( bar z _0)), w h e r eA is a constant, then prove that locus of z is a straight line.