The complex number z, satisfies the condition $\left|z-\frac{25}{z}\right|=24$  The maximum distance from the  origin of coordinates to the point  $z,$ is 

We have,   $\left|z\right|=\left|z+\frac{25}{z}-\frac{25}{z}\right|\le \left|z+\frac{25}{z}\right|+\left|\frac{25}{-z}\right|$

  $\begin{array}{l}\Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\left|z\right|\le 24+\frac{25}{\left|z\right|}\\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}|z{|}^2-24|z|-25\le 0\Rightarrow (\left|z\right|-25\left)\right(\left|z\right|+1)\le 0\\ \therefore \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\left|z\right|-25\le 0 [\because |z|+1>0] \\ \Rightarrow \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\left|z\right|\le 25\text{ or }|z-0|\le 25\end{array}$

Hence, the maximum distance from the origin of coordinates to

 the point z is 25.