For all complex numbers z1,z2  satisfying |z1|=12  and |z2−3−4i|=5 , the minimum value of |z1−z2|  is

|z1|=12 ⇒ z1  lies on circle with centre c1  at origin and radius 12                |z2−3−4i|=5⇒z2  lies on the circle with centre c2 (3+4i)  and radius 5.∴ |z1−z2|  will be minimum.If z1  and z2  lies on the line joining c1  and c2  i.e on the line z=3+4iMinimum value of |z1−z2|=AB=c1B−c1A=12−10=2