Let complex number z=x+ iy be such that frac{2 z-3 i}{2 z+i} is purely imaginary. If x + y ^2=0 , th

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4-1.Complex numbers

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Let the complex number $z=x+$ iy be such that $\frac{2 z-3 i}{2 z+i}$ is purely imaginary. If $x + y ^2=0$, then $y^4+y^2-y$ is equal to :

A

$\frac{3}{2}$

B

$\frac{4}{3}$

C

$\frac{2}{3}$

D

$\frac{3}{4}$

(JEE MAIN-2023)

Solution

$\frac{2 z-3 i}{2 z+i}$ is purely imaginary

$\therefore \frac{2 z-3 i}{2 z+i}+\frac{2 \bar{z}+3 i}{2 \bar{z}-i}=0$

$z=x+i y$

$\Rightarrow 4 x^2+4 y^2-4 y-3=0$

Given that $x+y^2=0$

$y^4+y^2-y=3 / 4$

Standard 11

Mathematics

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