Find the conjugate of each of the following:

Question:

Find the conjugate of each of the following

$\sqrt{-3}$

 

Solution:

Given: $z=\sqrt{-3}$

The above can be re – written as

$z=\sqrt{(-1) \times 3}$

$z=\sqrt{3 i^{2}}\left[\because \dot{\mathrm{i}}^{2}=-1\right]$

$z=0+\mathrm{i} \sqrt{3}$

So, the conjugate of $z=0+i \sqrt{3}$ is

$\bar{z}=0-i \sqrt{3}$

Or $\bar{z}=-i \sqrt{3}=-\sqrt{-3}$

 

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