WHAT IS THE PRINCIPAL SQUARE ROOT OF i??????

Question

abbles · Answer

The square root of i equals:

(square root of)2/2(1 + i)

anonymous · Answer

Would that become 0.71+i?

abbles · Answer

$$\sqrt{2}/2*(1 + i)$$

anonymous · Answer

or 0.71+0.71i ??

abbles · Answer

That is the simplified version. Here, this explains it well. Look under "square roots" .. http://en.wikipedia.org/wiki/Imaginary_unit

anonymous · Answer

Okay. :) 
I just need to know the simplified version of it and i'm not quite sure how to get it there. 
I have the options of 0.71+i, 0.71+0.71i, 3.14+0.71i, 1.414+i.
i know that the square root of 2 divided by 2 is 0.71. So would it be 0.71 + i ???

abbles · Answer

Simplified it would be 0.707106781 + 0.707106781 i, but you could round it to 0.71 + 0.71i.  You can get this by simplifying the answer I put earlier, and plugging it into Google calculator works, too.

anonymous · Answer

Oh! Wow, thank you soooo much!! @Abbles

abbles · Answer

no problem :)