When dealing with powers of complex numbers, always start by putting the quantity into exponential form.

i has a magnitude of 1 and an argument of π/2. Using Euler's formula,

i = exp(iπ/2)

Now the expression is in exponential form, taking the square root is easy, using basic exponential math.

sqrt(i) = (exp(iπ/2))^(1/2) = exp(iπ/4)

This quantity has a modulus of 1 and an argument of π/4. Using Euler's formula again,

sqrt(i) = (1 + i)/sqrt(2)