Hello
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.
You are correct, but you should have written above that P(i)=0
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.
Your division is correct and if it was a factor, your remainder would be 0.
The remainder is not zero so that is not a factor of the complex polynomial.
In (3) I attempted to use this method :
but I do know now how to this method with this question.
Notice this method states that the coefficients must be real (see "Think 1").
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.
Thanks
*note: should have read + i not +1 in title.