Answer:
[tex]-5-\sqrt{-44}=-5-2\sqrt{11}i[/tex]
Step-by-step explanation:
We want to simplify:
[tex]-5-\sqrt{-44}[/tex]
We rewrite the expression under the radical sign to obtain:
[tex]-5-\sqrt{4\times11\times -1}[/tex]
We split the expression under the radical sign to get:
[tex]-5-\sqrt{4} \times \sqrt{11} \times \sqrt{-1}[/tex]
Recall that:
[tex]\sqrt{-1}=i[/tex]
This implies that:
[tex]-5-\sqrt{4} \times \sqrt{11} \times \sqrt{-1}=-5-2\sqrt{11}i[/tex]
Therefore [tex]-5-\sqrt{-44}=-5-2\sqrt{11}i[/tex]
