Let the complex number z=x+iy be such that 2z−3i2z+iis purely imaginary. If x+y2=0 , then y4+y2-y is equal to

2z−3i2z+i ispurelyimaginary ∴2z−3i2z+i+2z¯+3i2z¯−i=0 Put z=x+iy we get x2+y2−y−34=0 using x+y2=0, ⇒y4+y2−y=34

Let the complex number z=x+iy be such that 2z−3i2z+iis purely imaginary. If x+y2=0 , then y4+y2-y is equal to

2z−3i2z+i ispurelyimaginary ∴2z−3i2z+i+2z¯+3i2z¯−i=0 Put z=x+iy we get x2+y2−y−34=0 using x+y2=0, ⇒y4+y2−y=34

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Let the complex number $z = x + i y$ 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

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$\frac{3}{4}$

$\frac{2}{3}$

$\frac{4}{3}$

$\frac{3}{2}$

answer is C.

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

$\begin{aligned} ∴ \frac{2 z - 3 i}{2 z + i} + \frac{2 \bar{z} + 3 i}{2 \bar{z} - i} = 0 \end{aligned} Put z = x + iy we get x^{2} + y^{2} - y - \frac{3}{4} = 0 u \sin g x + y^{2} = 0, \Rightarrow y^{4} + y^{2} - y = \frac{3}{4}$

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Let the complex number z=x+iy be such that 2z−3i2z+iis purely imaginary. If x+y2=0 , then y4+y2-y is equal to

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Let the complex number $z = x + i y$ 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