If z=x+i y, x y ≠ 0 , satisfies equation z^2+i bar{z}=0 , then left|z^2right| is equal to:

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4-1.Complex numbers

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If $z=x+i y, x y \neq 0$, satisfies the equation $z^2+i \bar{z}=0$, then $\left|z^2\right|$ is equal to:

A

$9$

B

$1$

C

$4$

D

$\frac{1}{4}$

(JEE MAIN-2024)

Solution

$ z^2=-i \bar{z} $

$ \left|z^2\right|=|i \bar{z}|$

$ \left|z^2\right|=|z|$

$ |z|^2-|z|=0$

$ |z|(|z|-1)=0$

$ |z|=0 \text { (not acceptable) } $

$ \therefore|z|=1 $

$ \therefore|z|^2=1$

Standard 11

Mathematics

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