If [tex]z=\pm 15i[/tex] has to be a solution of the equation, just plug it in:
[tex] (\pm 15i)^2 + [1] = 0 \iff -225 + [1] = 0 \iff [1] = 225 [/tex]
So, the solutions of
[tex] z^2+225=0[/tex]
are [tex] z=\pm 15i[/tex]
