I think it's because 2 doesn't qualify as a root.
If z - 3i is a factor of , find the remaining factors.
So I did this:
Step 1: if z - 3i is a factor, then z + 3i is a factor.
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Step 7:
Step 8:
Step 9:
Step 10: Find the factors from the quadratic.
Step 11:
Step 12:
Step 13:
Step 14:
Step 15:
So this is the answer I got, but the book says just that these are the two remaining factors without the leading 2, as follows:
(z - 1 + \frac{i}{\sqrt{2}})(z - 1 - \frac{i}{\sqrt{2}}
So did I get it wrong or is the 2 not really classified as part of the factor for some reason? I can't understand why the 2 isn't included in the answer in the back of the book.
David.
Your working is absolutely fine. The 2 is omitted as it's a constant term. I've struggled to explain why for a few minutes, with absolutely no success, however. I'll think about it, or perhaps else will help whilst I try to find the correct wording.
Edit: No need, courtesy of VonNemo