Imaginary Number Equation

(a+bi)^2=2i

then you expand to $\left(a^2-b^2\right)+2iab=2i$

$\left(a^2-b^2\right)+2iab=0+2i$

then, let's write is as system of equations: (I assume you know what it is)

$\begin{bmatrix}a^2-b^2=0\\ 2ab=2\end{bmatrix}$

So, $x=1+i,\:x=-1-i$

Hope this made sense! :D

-tigernathan