Question

5. Find the square rots of 4i.

Answer 1

`√(4i)=2√(i)`

Explanation:

`4i=4√(-1)`

Applying square root

`√(4i)`

`=\sqrt{4√(-1)}`

`=2\sqrt{√(-1)}`

`=2* -1^{(1)/(4)}`

Now,

`i=√(-1)\\\Rightarrow i=-1^{(1)/(2)}`

`\\\Rightarrow 2* -1^{(1)/(4)}=2* i^{(1)/(2)}=2√(i)`

So,
`√(4i)=2√(i)`