" If "|z-3|=3" ,then show that "(z-6)/(z)=i tan(arg z)

If complex numbers z_(1)z_(2) and z_(3) are such that |z_(1)| = |z_(2)| = |z_(3)| , then prove that arg((z_(2))/(z_(1)) = arg ((z_(2) - z_(3))/(z_(1) - z_(3)))^(2)

If complex numbers z_(1)z_(2) and z_(3) are such that |z_(1)| = |z_(2)| = |z_(3)| , then prove that arg((z_(2))/(z_(1))) = arg ((z_(2) - z_(3))/(z_(1) - z_(3)))^(2) .

For |z-1|=1, show that tan{(arg(z-1))/(2)}-((2i)/(z))=-i

If z_(1)=1+isqrt3and z_(2)=sqrt3-i, show that arg""(z_(1))/(z_(2))=argz_(1)-argz_(2).

If arg z = alpha and given that |z-1|=1, where z is a point on the argand plane , show that |(z-2)/z| = |tan alpha |,

If arg z = alpha and given that |z-1|=1, where z is a point on the argand plane , show that |(z-2)/z| = |tan alpha |,

if z_1=1+isqrt3 , z_2=sqrt3-i show that (a)arg (z_1z_2)=arg(z_1)+arg(z_2) and (b) arg(z_1//z_2)=arg(z_1)-arg(z_2)

If z_(1)=1+isqrt3and z_(2)=sqrt3-i, show that arg(z_(1)z_(2))=argz_(1)+argz_(2)

If z=(-1-i) , then arg z =