The question is Factorise z^3 +i over C . (Book's answer is (z-i)(z^2+iz-1))
I have attempted it 3 ways: Number 1 seems to work, but cannot get 2 or 3 to work.
Sorry I didnt know how to do long division in word so did it by hand instead.
In (1) I tried to divide z^3+i by (z-i) which I think is a factor
and this happened to give the same answer as the book.
In (2) I tried to divide z^3+i by (z+i) which I think is also a factor but I couldnt not complete the division properly.
In (3) I attempted to use this method :
but I do know now how to this method with this question.
Could you please correct my working and show me how to use method 3 if possible as I think that is the method the teacher wants us to do for these types of questions.
*note: should have read + i not +1 in title.
I thought that if z-i was a factor z+i would be too instead of if z-i is a root z+i is a root too, silly me.
Thank you for clearing that up