Question 5318
well, it is easy.

you need to find numbers a and b such that 

{{{ (a+bi)^2 = 0 + i }}}

{{{ a^2 + 2abi - b^2 = 0 + i}}}

the real parts and imaginary parts should match

{{{
  system( a^2-b^2 = 0, 
          2ab = 1
         )
}}}

{{{b = 1/2\a}}}

{{{a^2 - (1/2a)^2 = 0}}}
{{{a^2 = 1/(4a^2)}}}
{{{a^4 = 1/4}}}
{{{a^2 = 1/2}}} (another possibility, a^2 = -1/2, is senseless)
{{{a = 0+- 1/sqrt(2)}}}

Two solutions: {{{1/sqrt(2)+i/sqrt(2)}}}, {{{-1/sqrt(2)-i/sqrt(2)}}}