A variable complex number `z=x+iy` is such that arg `(z-1)/(z+1)= pi/2`. Show that `x^2+y^2-1=0`.

If z=x+ iy such that the argument of (z-1)/(z+1) is always pi/4 . Prove that x^2 + y^2-2y=1

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

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=-( z )_2dot

If z and w are two complex number such that |zw|=1 and arg (z) – arg (w) = pi/2, then show that overline zw = -i.

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=- bar z _2dot

Statement-1 : let z_(1) and z_(2) be two complex numbers such that arg (z_(1)) = pi/3 and arg(z_(2)) = pi/6 " then arg " (z_(1) z_(2)) = pi/2 and Statement -2 : arg(z_(1)z_(2)) = arg(z_(1)) + arg(z_(2)) + 2kpi, k in { 0,1,-1}

Let Z and w be two complex number such that |zw|=1 and arg(z)−arg(w)=pi//2 then

If z be any complex number (z!=0) then arg((z-i)/(z+i))=pi/2 represents the curve

If complex number z=x +iy satisfies the equation Re (z+1) = |z-1| , then prove that z lies on y^(2) = 4x .

If z_1 and z_2 are two complex numbers such that |\z_1|=|\z_2|+|z_1-z_2| show that Im (z_1/z_2)=0