If z is a complex number satisfying - z 3- z -3- - 2- then the maximum possible value of - z - z -1- isA- 2 B- -2- 2 -2D- 1

|z^3 + z^–3|≤ 2 Let, |z + z^–1| = a |(z + z^–1)^3 | = a^3 |z^3 + z^–3 + 3(z + z^–1)| =a^3 |z^3 + z^–3| + 3a ≥ a^3 ⇒ a^3 3a≤ 2 ⇒ a^3 3a 2≤ 0 (a 2)(a+1)^2≤ 0 n ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Equality of 2 Complex Numbers

If z is a com...

Question

If $z$ is a complex number satisfying $| z^{3} + z^{- 3} | \leq 2,$ then the maximum possible value of $| z + z^{- 1} |$ is

2

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\sqrt[3]{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 \sqrt{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $2$
$| z^{3} + z^{- 3} | \leq 2$
Let, $| z + z^{- 1} | = a | (z + z^{- 1})^{3} | = a^{3}$
$| z^{3} + z^{- 3} + 3 (z + z^{- 1}) | = a^{3}$
$| z^{3} + z^{- 3} | + 3 a \geq a^{3}$
$\Rightarrow a^{3} - 3 a \leq 2 \Rightarrow a^{3} - 3 a - 2 \leq 0$
$(a - 2) (a + 1)^{2} \leq 0$
$| z + z^{- 1} | = a \leq 2$
$| z + z^{- 1} |_{m a x} = 2$

Suggest Corrections

Similar questions

Q. If z is a complex number satisfying

| z^{3} + z^{- 3} | \leq 2

,then the maximum possible value of

| z + z^{- 1} |

Q. If

z

is a complex number satisfying

| z^{3} + z^{- 3} | \leq 2

, then the maximum possible value of

| z + z^{- 1} |

Q. If

z

is a complex number satisfying

| z - 3 - 2 i | \leq 1

, then the maximum value of

| i z + 2 |

If z be a complex number satisfying $z^{4}$ + $z^{3}$ + $2 z^{2}$ + z + 1 = 0 Then the value of $| z |$ .

$θ$ ∈ [0, 2 $π$ ] and $z_{1}, z_{2}, z_{3}$ are three complex numbers such that they are collinear and

$(1 + | s i n θ |) z_{1}$ + $(| c o s θ | - 1) z_{2}$ - $\sqrt{2}$ $z_{3}$ =0. If at least one of the complex numbers $z_{1}, z_{2}, z_{3}$ is

non-zero then number of possible values of $θ$ is

Join BYJU'S Learning Program

If z is a complex number satisfying |z3+z−3|≤2, then the maximum possible value of |z+z−1| is

The correct option is A 2|z3+z–3|≤2 Let, |z+z–1|=a|(z+z–1)3|=a3 |z3+z–3+3(z+z–1)|=a3 |z3+z–3|+3a≥a3 ⇒a3−3a≤2⇒a3−3a−2≤0 (a−2)(a+1)2≤0 |z+z−1|=a≤2 |z+z−1|max=2

If $z$ is a complex number satisfying $| z^{3} + z^{- 3} | \leq 2,$ then the maximum possible value of $| z + z^{- 1} |$ is