
Complex equation
$\displaystyle iz^2z+i=0$
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.

By the Fundamental Theorem of Algebra, this equation has two complex roots. They might be repeated, but there is definitely a solution. I would use the quadratic formula. It's still valid even when the coefficients are complex.

Ah, yes, I see. For anyone who's wondering, the roots are $\displaystyle (\frac{1}{2}+\frac{1}{2}\sqrt{5})i$ and $\displaystyle (\frac{1}{2}\frac{1}{2}\sqrt{5})i$
Thanks a lot!

You're very welcome. Have a good one!

I think your roots are the opposite sign of what they should be. I would doublecheck them.