The complex number z satisfies the condition | vedclass

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(A) Let $|z| = r$. Given $\left| z - \frac{25}{z} \right| = 24$.Using the triangle inequality property $||z_1| - |z_2|| \leq |z_1 - z_2| \leq |z_1| +

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$25$

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(A) Let $|z| = r$. Given $\left| z - \frac{25}{z} \right| = 24$.Using the triangle inequality property $||z_1| - |z_2|| \leq |z_1 - z_2| \leq |z_1| + |z_2|$,we have:$|z| - \frac{25}{|z|} \leq \left| z - \frac{25}{z} \right| \leq |z| + \frac{25}{|z|}$.From the right side of the inequality: $24 \leq r + \frac{25}{r} \implies r^2 - 24r + 25 \geq 0$.From the left side of the inequality: $r - \frac{25}{r} \leq 24 \implies r^2 - 24r - 25 \leq 0$.Solving $r^2 - 24r - 25 = 0$,we get $(r - 25)(r + 1) = 0$. Since $r > 0$,$r \leq 25$.Thus,the maximum value of $|z|$ is $25$.

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:

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