What is the Value of √i + √-i?

[kini.Amith]

Homework Statement

The value of √i + √-i , where i=√-1 is
(a) 0 (b) 1/√2 (c) √2 (d) -√2

Only one option can be chosen

Homework Equations

The Attempt at a Solution

Let (x + iy)²=i
Solving for x and y, I got
√i = +1/√2 (1+i) or -1/√2 (1+i)

Similarly i got
√-i = +1/√2 (1-i) or -1/√2 (1-i)

Now how do I calculate, √i - √-1,
i.e since there 2 possible values for each √i and √-i , which do i subtract from which?

Using another method I got the final nswer as + or - √2 , but u can only choose one of the given options

 

[D H]

They are asking for the principal square root.

 

[kini.Amith]

They are asking for the principal square root.

How are principal square roots defined for imaginary numbers?
For eg, if you have 1 - i and -1 + i as the 2 square roots, which do you choose as the principal one?
If you have i and -i, which do you choose?

 

[vela]

Have you tried looking up the definition in your textbook or notes?