Complex number|Find the locus of equation if arg(z-1/z+3)=π/2|Alternative method|K.Thirumurugan

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A-level Mathematics 9709: Argand diagrams and loci A-level Mathematics 9709: Argand diagrams and loci
Show that the complex number z, satisfying the condition arg (z-1/z+1) = π/4 lies on a circle. Show that the complex number z, satisfying the condition arg (z-1/z+1) = π/4 lies on a circle.
Show that the complex number z satisfying the condition Show that the complex number z satisfying the condition 'arg(z-1/z+1)=pi/4' lies on a circle'
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If `arg((z-1)/(z+1))=pi/2` then the locus of z is If `arg((z-1)/(z+1))=pi/2` then the locus of z is
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