Posted by **Anonymous** on Monday, October 24, 2011 at 5:06pm.

How would you use synthetic division to find the quotient and remainder for this problem:

(X^3+3ix^2-4ix-2)/(x+i)

- College Algrebra -
**Steve**, Monday, October 24, 2011 at 5:41pm
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.

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