The complex number z Re z -2- satisfies the equation z 2-4 z - z -2-16- z -3- then the value of - z -4 isA- 1B- 4C- 256D- 16

Let z=x+iy x^2 y^2+2ixy=4x+4iy+a, where a is a real number ⇒ 2xy=4y (equating the imaginary part) ⇒ y=0 (∵ x≠2) ⇒ z=x x^2=4x+x^2 16x^3 ⇒ 4x 16x^3=0 ⇒ x^4=4 ⇒ | ...

Sum of Infinite Terms of a GP

The complex n...

Question

The complex number $z (R e (z) \neq 2)$ satisfies the equation $z^{2} = 4 z + | z |^{2} - \frac{16}{| z |^{3}},$ then the value of $| z |^{4}$ is

1

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

4

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

16

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

256

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

Open in App

Solution

The correct option is B $4$
Let $z = x + i y$
$x^{2} - y^{2} + 2 i x y = 4 x + 4 i y + a, where a is a real number$
$\Rightarrow 2 x y = 4 y (equating the imaginary part) \Rightarrow y = 0 (∵ x \neq 2) \Rightarrow z = x$

$x^{2} = 4 x + x^{2} - \frac{16}{x^{3}} \Rightarrow 4 x - \frac{16}{x^{3}} = 0 \Rightarrow x^{4} = 4 \Rightarrow | z |^{4} = 4$

Suggest Corrections

Similar questions

Q. If complex number

z (z \neq 2)

satisfies the equation

z^{2} = 4 z + {| z |}^{2} + \frac{1}{{| z |}^{3}}

, then the value of

{| z |}^{- 4}

Q. Let Z be a complex number satisfying the equation

(Z^{3} + 3)^{2} = - 16

then |Z| has the value equal to

Q. The complex number z satisfies the equation z + |z| = 2 + 8i. Then the value of |z| is

The complex number Z satisfies the equation Z + $| Z |$ = 2+8i, then the value of $| Z |$ - 8 is

___

Q. Consider a complex number

z

which satisfies the equation

∣ ∣ ∣ z - (\frac{4}{z}) ∣ ∣ ∣ = 2

, then the value of

a r g (\frac{z_{1}}{z_{2}})

, where

z_{1}

and

z_{2}

are complex numbers with the greatest and the least moduli, can be

Join BYJU'S Learning Program

Select...

The complex number z (Re(z)≠2) satisfies the equation z2=4z+|z|2−16|z|3, then the value of |z|4 is

The correct option is B 4Let z=x+iy x2−y2+2ixy=4x+4iy+a, where a is a real number ⇒2xy=4y (equating the imaginary part)⇒y=0 (∵x≠2)⇒z=x x2=4x+x2−16x3⇒4x−16x3=0⇒x4=4⇒|z|4=4

The complex number $z (R e (z) \neq 2)$ satisfies the equation $z^{2} = 4 z + | z |^{2} - \frac{16}{| z |^{3}},$ then the value of $| z |^{4}$ is