Locus of z ; if `arg(z)=theta` (=constant)

Locus of z; if (z-a)=theta(= cons tan t) and a>0

Trace the locus of z if arg(z+i)=(-pi)/(4)

Locus of z if arg[z-(1+i)]={(3 pi)/(4) when |z| |z-4| is

Statement-1 : The locus of z , if arg((z-1)/(z+1)) = pi/2 is a circle. and Statement -2 : |(z-2)/(z+2)| = pi/2 , then the locus of z is a circle.

Find the locus of z if arg ((z-1)/(z+1))= pi/4

In argand plane |z| represent the distance of a point z from the origin. In general |z_(1)-z_(2)| represent the distance between two points z_(1) and z_(2) . Also for a general moving point z in argand plane, if arg(z)=theta , then z=|z|e^(i theta) , where e^(i theta)=cos theta+i sin theta . If |z-(3+2i)|=|z cos((pi)/(4)-"arg z")| , then locus of z is

Complex numbers z_(1) and z_(2) lie on the rays arg(z1) =theta and arg(z1) =-theta such that |z_(1)|=|z_(2)| . Further, image of z_(1) in y-axis is z_(3) . Then, the value of arg (z_(1)z_(3)) is equal to