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Find the modulus of each of the following:

Question:

Find the modulus of each of the following:

$(3+\sqrt{-5})$

 

Solution:

Given: $z=(3+\sqrt{-5})$

The above can be re - written as

$z=3+\sqrt{(-1) \times 5}$

$z=3+i \sqrt{5}\left[\because i^{2}=-1\right]$

Now, we have to find the modulus of (3 + i√5)

So, $|z|=|3+i \sqrt{5}|=\sqrt{(3)^{2}+(\sqrt{5})^{2}}=\sqrt{9+5}=\sqrt{14}$

Hence, the modulus of $(3+\sqrt{-5})$ is $\sqrt{14}$

 

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