JEE Main · MathematicsHard

$If z is a complex number such that ∣ z - 3 - 2 i ∣ = 2, then the maximum value of ∣2 z - 6 + 5 i ∣ is$

A. $11$
B. $12$
C. $13$
D. $14$

Show correct answer & step-by-step solution

Correct answer: A — $11$

Solution

Rewrite the expression as $2|z - 3 + 2.5i|$. Using the triangle inequality, the maximum value is $2(|z - 3 - 2i| + |2i - 2.5i|)$, which simplifies to $2(2 + 3.5) = 11$.

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If z is a complex number such that |z - 3 - 2i| = 2, then the maximum value of |… — JEE Main Mathematics Question with Solution |