Answer:
[tex]\sqrt{4i}=2\sqrt{i}[/tex]
Step-by-step explanation:
[tex]4i=4\sqrt{-1}[/tex]
Applying square root
[tex]\sqrt{4i}[/tex]
[tex]=\sqrt{4\sqrt{-1}}[/tex]
[tex]=2\sqrt{\sqrt{-1}}[/tex]
[tex]=2\times -1^{\frac{1}{4}}[/tex]
Now,
[tex]i=\sqrt{-1}\\\Rightarrow i=-1^{\frac{1}{2}}[/tex]
[tex]\\\Rightarrow 2\times -1^{\frac{1}{4}}=2\times i^{\frac{1}{2}}=2\sqrt{i}[/tex]
So, [tex]\sqrt{4i}=2\sqrt{i}[/tex]
