posted by Anonymous .
How would you use synthetic division to find the quotient and remainder for this problem:
The same way you do it normally. Just keep track of the i's and remember that -i^2 = 1
So, the rows of coeffiicients are (munged by font spacing)
1 3i -4i -2 (i
0 i -4 -4i+4
1 4i -4-4i 2-4i
So that means that
(x^3 + 3ix^2 - 4ix - 2)/(x-i)
= x^2 + 4ix - (4+4i) remainder 2-4i
If you multiply it out, it works.