Complex roots of Complex polynomal

Question

Apologies if this is a repeated thread I just couldn't quite find anything that helped.

how do I go about finding the complex roots of a complex polynomial? such as

$$x^3 + (1-i)x^2 + (1-i)x - i$$

any advice would be great thanks

Answer 1

There is a general formula for that. However, in this case you can also notice, that $x=i$ is clearly a solution, and then divide the polynomial by $x-i$ to get:

$$\left(x-i\right)\left(x^{2}+x+1\right)=0$$

The other two roots can then be found by solving $x^2+x+1$