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Algebra of complex numbers

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By Expert Faculty of Sri Chaitanya

Question

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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Solution

We have, $| z | = |z + \frac{25}{z} - \frac{25}{z}| \leq |z + \frac{25}{z}| + |\frac{25}{- z}|$
$\begin{array}{lr} \Rightarrow | z | \leq 24 + \frac{25}{| z |} \\ \Rightarrow | z |^{2} - 24 | z | - 25 \leq 0 \Rightarrow (| z | - 25) (| z | + 1) \leq 0 \\ ∴ | z | - 25 \leq 0 [∵ | z | + 1 > 0] \\ \Rightarrow | z | \leq 25 or | z - 0 | \leq 25 \end{array}$
Hence, the maximum distance from the origin of coordinates to
the point z is 25.

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Similar Questions

Let $i = \sqrt{- 1}$ , define a sequence of a complex number by $z_{1} = 0, z_{n + 1} = z_{n}^{2} + i for n \geq 1$ .In the complex plane, how far from the origin z₁₁₁ ?

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