Mathematics - Complex Number Question with Solution | TestHub

Given
$sz+t\stackrel{-}{z}+r=0$...(i)
On taking conjugate$\stackrel{-}{s}\stackrel{-}{z}+\stackrel{-}{t}z+\stackrel{-}{r}=0$...(ii)
$z\left({\left|s\right|}^2-{\left|t\right|}^2\right)=\stackrel{-}{r}t-r\stackrel{-}{s}$
$\left(1\right)$If$\left|s\right|\ne \left|t\right|$then$z$has unique value
$\left(2\right)$If$\left|s\right|=\left|t\right|$then$\stackrel{-}{r}t-r\stackrel{-}{s}$may or may not be zero so$L$may be empty set
$\left(3\right)$Locus of$z$is null set or singleton set or a line in all cases it will intersect given circle at most two points.
$\left(4\right)$In this case locus of$z$is a line so$L$has infinite elements