Find the square roots of the following: `1+i`

Answer

`sqrt(1+i) = pm sqrt((sqrt2+1)/2) + i sqrt((sqrt2-1)/2)`

Explanation

`sqrt(1+i) = x+iy`

Squaring, we get

`1+i=x^2−y^2+2ixy`

`therefore x^2−y^2=1,2xy=1`

`therefore (x^2+y^2)^2=(x^2−y^2)^2+4x^2 y^2=1+1=2`

`therefore x^2+y^2=sqrt(2)​ and x^2−y^2=1`

On adding and subtracting the above equations , we get

On adding and subtracting the above equations , we get

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