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

If |(1-iz)/(z-i)|=1 find the locus of z

If |(1-iz)/(z-i)|=1 find the locus of z

If Im((z-i)/(2i))=0 then the locus of z is

If |z-3i|=|z+3i| , then find the locus of z.

If (z+i)/(z+2i) is purely real then find the locus of z

If Im((z-1)/(2z+1))=-4, then locus of z is

If z=x+iy, x,y in R such that z!=1 and |z-1|!=1. If (z-1)/(e^((i pi)/(3)))+(e^((i pi)/(3)))/(z-1) is real, then locus of z is a straight line whose slope is

If arg((z-1)/(z+1))=(pi)/(2) then the locus of z is