If z is purely real ; then `arg(z)=0 or pi`

If z is purely imaginary ; then arg(z)=+-(pi)/(2)

If z is not purely real then area bounded by curves Img(z+1/z)=0 & |z-1| = 2 is(in square units)-

If (z+i)/(z+2i) is purely real then find the locus of z

If z is a purely real complex number such that "Re"(z) lt 0 , then, arg(z) is equal to

If z is purely imaginary and Im (z) lt 0 , then arg(i bar(z)) + arg(z) is equal to

If z = (3+isintheta)/(4-icostheta) is purely real and theta in (pi/2,pi) ,then arg(sintheta + i costheta) is -

If |z_1|=|z_2| and arg(z_1)+arg(z_2)=pi/2 then (A) z_1z_2 is purely real (B) z_1z_2 is purely imaginary (C) (z_1+z_2)^2 is purely imaginary (D) arg(z_1^(-1))+arg(z_2^(-1))=-pi/2

If arg(z+a) = pi//6 and arg(z-a) = 2 pi//3 (a in R^(+)) , then

If arg(z) lt 0, then find arg(-z) -arg(z) .