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

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.

The locus of the points z satisfying the condition arg ((z-1)/(z+1))=pi/3 is, a

Find the value of z, if |z |= 4 and arg (z) = (5pi)/(6) .

Statement-1: If z_(1),z_(2) are affixes of two fixed points A and B in the Argand plane and P(z) is a variable point such that "arg" (z-z_(1))/(z-z_(2))=pi/2 , then the locus of z is a circle having z_(1) and z_(2) as the end-points of a diameter. Statement-2 : arg (z_(2)-z_(1))/(z_(1)-z) = angleAPB

If z=x +i y such that |z+1|=|z-1| and arg((z-1)/(z+1))=pi/4 , then find zdot

Find the locus of a complex number z= x+ yi satisfying the relation arg (z-a)=(pi)/(4), a in R Illustrate the locus of z in the Argand plane

Find the locus of a complex number z such that arg ((z-2)/(z+2))= (pi)/(3)

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

If z = x + iotay and amp((z-1)/(z+1)) = pi/3 , then locus of z is

What is the locus of z if ||z-cos^(-1)cos12|-|z-sin^(-1)s in 12||=8(pi-3)?