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

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

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)

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

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

If for complex numbers z_1 and z_2 , arg(z_1) - arg(z_2)=0 , then show that |z_1-z_2| = | |z_1|-|z_2| |

If the complex number Z_(1) and Z_(2), arg (Z_(1))- arg(Z_(2)) =0 . then show that |z_(1)-z_(2)| = |z_(1)-z_(2)| .