Find all possible values of `sqrt(i)+sqrt(-i)dot`

Explanation

`sqrt(i) + sqrt(-i) = sqrt(0+1.i)+sqrt(0-1.i)`
Now`sqrt(a+i.b) = {sqrt((1)/(2){sqrt(a^(2)+b^(2))+a})+ isqrt((1)/(2){sqrt(a^(2)+b^(2))-a})}`
`and sqrt(a-i.b) =om{sqrt((1)/(2){sqrt(a^(2)+b^(a))+a}-i)sqrt((1)/(2){sqrt(a^(2)+b^(2))-a})}`
`rArr sqrt(0+1.i) = pm{sqrt((1)/(2){sqrt(0 +1^(2)) +0})+isqrt((1)/(2){sqrt(0+1^(2)) -0})}`
`= pm (1)/(sqrt(2)) (1-i)`
` and sqrt(0-1.i)= pm {sqrt((1)/(2) {sqrt(0+1^(2))+0})-isqrt((1)/(2){sqrt(0+1^(2))-0})}`
` = pm (1)/(sqrt(2)) (1-i)`
Now ` sqrt(i) + sqrt(-i) = pm (1)/(sqrt(2)) (1+i) pm (1)/(sqrt(2))(1-i)`
`or sqrt(i) + sqrt(-i) =pmsqrt(2) + 0.ior 0pm sqrt(2i)`