# Complex equation

• Jun 25th 2010, 11:21 AM
Pim
Complex equation
$iz^2-z+i=0$
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:
$z^2+zi+1=0$
But I can't see how I could factorise this.

• Jun 25th 2010, 11:33 AM
Ackbeet
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.
• Jun 25th 2010, 09:45 PM
Pim
Ah, yes, I see. For anyone who's wondering, the roots are $(\frac{1}{2}+\frac{1}{2}\sqrt{5})i$ and $(\frac{1}{2}-\frac{1}{2}\sqrt{5})i$

Thanks a lot!
• Jun 26th 2010, 02:04 AM
Ackbeet
You're very welcome. Have a good one!
• Jun 26th 2010, 05:24 AM
Ackbeet
I think your roots are the opposite sign of what they should be. I would double-check them.