(B) Given the equation $z^2 + i\bar{z} = 0$,we have $z^2 = -i\bar{z}$.Taking the modulus on both sides,we get $|z^2| = |-i\bar{z}|$.Since $|-i| = 1$ a

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(B) Given the equation $z^2 + i\bar{z} = 0$,we have $z^2 = -i\bar{z}$.Taking the modulus on both sides,we get $|z^2| = |-i\bar{z}|$.Since $|-i| = 1$ and $|\bar{z}| = |z|$,this simplifies to $|z|^2 = |z|$.This implies $|z|^2 - |z| = 0$,or $|z|(|z| - 1) = 0$.Since $xy \neq 0$,$z \neq 0$,so $|z| \neq 0$. Thus,$|z| = 1$.Therefore,$|z^2| = |z|^2 = 1^2 = 1$.

Class 11 Mathematics 4-1.Complex numbers Conjugate and Modulus of complex numbers

Medium

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

JEE MAIN 2024 All JEE MAIN

A
$9$
B
$1$
C
$4$
D
$1/4$

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4-1.Complex numbers

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Conjugate and Modulus of complex numbers

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