The modulus of the square root of the conjuga | vedclass

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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 $\bar{z}$,

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$5$

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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,$|\sqrt{\bar{z}}| = \sqrt{25} = 5$.

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

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