$\displaystyle iz^2-z+i=0$

Are there solutions to this equation? If yes, how could I calculate it/them?

This was a question on a test I had and I suspect it was a typo, though I still would like to know how to solve it.

I tried multiplying by -i, this gives:

$\displaystyle z^2+zi+1=0$

But I can't see how I could factorise this.

Thanks in advance.