If z−4z=2, then the maximum value of zis equal to

|z|−4|z|≤||z−4|z|≤z−4z=2⇒                         |z|2−2|z|−4≤0⇒        (|z|−1)2≤5⇒|z|≤1+5.The maximum value 5+1 is attained when z=5+1.