jovanyalvarez71 jovanyalvarez71
  • 21-10-2019
  • Mathematics
contestada

5. Find the square rots of 4i.

Respuesta :

boffeemadrid
boffeemadrid boffeemadrid
  • 22-10-2019

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]

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