`arg(1/barz)=arg((zbarz)/(barz))`

arg(bar(z))=-arg(z)

arg((z)/(bar(z)))=arg(z)-arg(bar(z))

If z satisfies the equation ((z-2)/(z+2))((barz-2)/(barz+2))=1 , then minimum value of |z| is equal to :

If -pi

The value of sqrt({arg(z)+arg(-bar(z))-2 pi}{arg(-z)+arg(bar(z))})AA z=x+iy,x,y>0 is

Suppose arg (z) = - 5 pi//13 , then arg((z + bar(z))/(1+z bar(z))) is

If : barx+bary+barz=0,abs(barx)=abs(bary)=abs(barz)=2 and mangle(bary,barz)=theta , then : cos^(2)theta+cot^(2)theta=

If z, z_1 and z_2 are complex numbers, prove that (i) arg (barz) = - argz (ii) arg (z_1 z_2) = arg (z_1) + arg (z_2)