If `I m((z-1)/(e^(thetai))+(e^(thetai))/(z-1))=0` , then find the locus of `z`

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

If |(z-i)/(z+i)|=1 , then the locus of z is

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

If |z-3+i|=4 , then the locus of z is

If w=z/[z-(1/3)i] and |w|=1, then find the locus of z

If |z-z_(1)|=|z-z_(2)| then the locus of z is :

If a rg(z_1)=170^0a n d arg(z_2)=70^0 , then find the principal argument of z_1z_2dot

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

If z=((sqrt(3)+i)^(17))/((1-i)^(50)) , then find a m p(z)dot

If the angle between the plane x-3y+2z=1 and the line (x-1)/2=(y-1)/1=(z-1)/(-3)i stheta, then the find the value of cos e cthetadot