Let complex number z be such that |z- frac{6}{z}|=5 then maximum value of |z| will be -

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4-1.Complex numbers

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Let complex number $z$ be such that $|z- \frac{6}{z}|=5$ then maximum value of $|z|$ will be -

A

$2$

B

$3$

C

$5$

D

$6$

Solution

$\left|z-\frac{6}{z}\right| \geq|z|-\frac{6}{|z|} \Rightarrow 5 \geq|z|-\frac{6}{|z|}$

$\Rightarrow|z|^{2}-5|z|-6 \leq 0$

$\Rightarrow|z| \in[-1,6]$

$\therefore$ maximum value $=6$

Standard 11

Mathematics

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