Question

5. Find the square rots of 4i.

Answer 1

Answer:

$\sqrt{4i}=2\sqrt{i}$

Step-by-step explanation:

$4i=4\sqrt{-1}$

Applying square root

$\sqrt{4i}$

$=\sqrt{4\sqrt{-1}}$

$=2\sqrt{\sqrt{-1}}$

$=2\times -1^{\frac{1}{4}}$

Now,

$i=\sqrt{-1}\\\Rightarrow i=-1^{\frac{1}{2}}$

$\\\Rightarrow 2\times -1^{\frac{1}{4}}=2\times i^{\frac{1}{2}}=2\sqrt{i}$

So, $\sqrt{4i}=2\sqrt{i}$