(D) Let $z = -7 + 24i$,where $i = \sqrt{-1}$.The conjugate of $z$ is $\bar{z} = -7 - 24i$.We need to find the modulus of the square root of $\bar{z}$,

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(D) Let $z = -7 + 24i$,where $i = \sqrt{-1}$.The conjugate of $z$ is $\bar{z} = -7 - 24i$.We need to find the modulus of the square root of $\bar{z}$,which is $|\sqrt{\bar{z}}|$.Using the property of modulus,$|\sqrt{\bar{z}}| = \sqrt{|\bar{z}|}$.The modulus of $\bar{z}$ is $|\bar{z}| = \sqrt{(-7)^2 + (-24)^2} = \sqrt{49 + 576} = \sqrt{625} = 25$.Therefore,$|\sqrt{\bar{z}}| = \sqrt{25} = 5$.

Class 11 Mathematics 1 Complex Numbers and Quadratic Equations: Complex Numbers Conjugate and Modulus of complex numbers

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The modulus of the square root of the conjugate of $-7+24 \sqrt{-1}$ is ....

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$3$
B
$4$
C
$16$
D
$5$

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1 Complex Numbers and Quadratic Equations: Complex Numbers

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Conjugate and Modulus of complex numbers

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Let $z$ be a complex number such that $|z|+z=2+i$,where $i=\sqrt{-1}$. Then $|z|$ is equal to:

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If ${z_1}, {z_2} \in \mathbb{C}$,then which of the following is true?

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If $Z_1$ and $Z_2$ are conjugate complex numbers, match the items in Column-$I$ with Column-$II$:
Column-$I$ Column-$II$
$A. Z_1 Z_2$ $1. \text{imaginary axis}$
$B. Z_1 + Z_2 = 0$ $2. \text{Im}(-Z_2)$
$C. \text{Im}(Z_1)$ $3. |Z_1|^2$
$D. \text{Re}(Z_1)$ $4. \text{Re}(Z_2)$

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If $|z| = 1$ and $\omega = \frac{z - 1}{z + 1}$ (where $z \neq -1$),then $\text{Re}(\omega)$ is

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If the conjugate of $(x + iy)(1 - 2i)$ is $1 + i$,then

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Column-$I$	Column-$II$
$A. Z_1 Z_2$	$1. \text{imaginary axis}$
$B. Z_1 + Z_2 = 0$	$2. \text{Im}(-Z_2)$
$C. \text{Im}(Z_1)$	$3. \|Z_1\|^2$
$D. \text{Re}(Z_1)$	$4. \text{Re}(Z_2)$

The modulus of the square root of the conjugate of $-7+24 \sqrt{-1}$ is ....

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Let $z$ be a complex number such that $|z|+z=2+i$,where $i=\sqrt{-1}$. Then $|z|$ is equal to:

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If $Z_1$ and $Z_2$ are conjugate complex numbers, match the items in Column-$I$ with Column-$II$:Column-$I$Column-$II$$A. Z_1 Z_2$$1. \text{imaginary axis}$$B. Z_1 + Z_2 = 0$$2. \text{Im}(-Z_2)$$C. \text{Im}(Z_1)$$3. |Z_1|^2$$D. \text{Re}(Z_1)$$4. \text{Re}(Z_2)$

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If $Z_1$ and $Z_2$ are conjugate complex numbers, match the items in Column-$I$ with Column-$II$:
Column-$I$ Column-$II$
$A. Z_1 Z_2$ $1. \text{imaginary axis}$
$B. Z_1 + Z_2 = 0$ $2. \text{Im}(-Z_2)$
$C. \text{Im}(Z_1)$ $3. |Z_1|^2$
$D. \text{Re}(Z_1)$ $4. \text{Re}(Z_2)$