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Find the square roots of the following: ...

Find the square roots of the following: `i`

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The correct Answer is:
`sqrt(i) = pm 1/sqrt(2) (1+i)`
Let `sqrt(i)​=x+iy`.
Then `i=x^2-y^2+2ixy`,
`therefore` `x^2-y^2=0` and `2xy=1`.
Solving these, we get `x=y=pm 1/sqrt(2)`​.
Thus,
`sqrt(i) = pm(1/sqrt(2) + 1/sqrt(2) i) = pm 1/sqrt(2) (1+i)`
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