The complex number z, satisfies the condition z−25z=24  The maximum distance from the  origin of coordinates to the point  z, is

We have,   |z|=z+25z−25z≤z+25z+25−z  ⇒    |z|≤24+25|z|⇒    |z|2−24|z|−25≤0⇒(|z|−25)(|z|+1)≤0            ∴    |z|−25≤0                                                       [∵|z|+1>0]                                   ⇒    |z|≤25 or |z−0|≤25Hence, the maximum distance from the origin of coordinates to the point z is 25.