Let us consider all complex numbers satisfying |z−25i|≤15.Among all these complex numbers :

⇒θmim=∠AOX=tan−1⁡1520=tan−1⁡34⇒θmax=∠DOX=π−tan−1⁡34⇒OEmin=10, OBmax=40

Let us consider all complex numbers satisfying |z−25i|≤15.Among all these complex numbers :

⇒θmim=∠AOX=tan−1⁡1520=tan−1⁡34⇒θmax=∠DOX=π−tan−1⁡34⇒OEmin=10, OBmax=40

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Let us consider all complex numbers satisfying $| z - 25 i | \leq 15$ .Among all these complex numbers :

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least argument of Complex number is $\tan^{- 1} (3 / 4)$

maximum argument of Complex number is $π - \tan^{- 1} (3 / 4)$

Complex number least magnitude is 10i

Complex number with maximum magnitude is 40i

answer is A, B, C, D.

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$\begin{array}{l} \Rightarrow θ_{mim} = ∠ A O X = \tan^{- 1} \frac{15}{20} = \tan^{- 1} \frac{3}{4} \\ \Rightarrow θ_{max} = ∠ D O X = π - \tan^{- 1} \frac{3}{4} \\ \Rightarrow {OE}_{min} = 10, OB max = 40 \end{array}$

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Let us consider all complex numbers satisfying |z−25i|≤15.Among all these complex numbers :

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Let us consider all complex numbers satisfying $| z - 25 i | \leq 15$ .Among all these complex numbers :