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

Question

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

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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 $$25$$.

Algebra of complex numbers

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

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Algebra of complex numbers

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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.

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