If |z- 4z |=2, then the maximum value of |z| is (a) 5+1 (b) 2 (c) 2+ 2 (d) 3+1

Correct answer: (a) 5+1 |z|- 4 |z| ≤ |z- 4z |=2, so with r=|z|, r²-2r-4 0→ r 1+ 5. JEE Main 2009 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

JEE PYQ

[JEE Main 2009] if z 4z 2 then the maximum value of z is

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If $\left|z-\dfrac4z\right|=2$, then the maximum value of $|z|$ is

(a) $\sqrt5+1$
(b) $2$
(c) $2+\sqrt2$
(d) $\sqrt3+1$

1 Answer

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

Correct answer: (a) $\sqrt5+1$

$|z|-\frac4{|z|}\le\left|z-\frac4z\right|=2$, so with $r=|z|$, $r^2-2r-4\le0\Rightarrow r\le1+\sqrt5$.

JEE Main 2009 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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