STUFF I HAD TO DELETE FROM A WRITING PROBLEM

    So I was doing a writing problem, and I realized that I did something wrong. That meant that I had to delete everything that I wrote. And I didn't want 30 mins of work to just go into the garbage, so I decided to post it on here!

Let's first define $z$

$$z=a+bi$$
so
$$-2\bar z=2a-2bi$$
and
$$iz=i(a+bi)$$
$$\Longrightarrow ia+bi^2$$
$$\Longrightarrow ia-b$$
and
$$|z|^2=(\sqrt{a^2+(b)^2)^2}$$
$$\Longrightarrow a^2+b^2$$

So now the full equation is:
$$a^2+b^2-(2a-2bi)+(ia-b)=2i$$
$$a^2-2a+b^2-b+ia+2bi-2i=0$$
$$a^2-2a+b^2-b+i(a+2b-2)=0$$