How do I solve x^4 + 8x^2 + 26ix - 20 / x-4i using synthetic division?

Question

I know you have to fill in zeros where the exponents are not in desending order and I know how to do the synthetic division part of it. But whats up with the imaginary # (i) How do I solve it with that? I hope someone can help.

Answer 1

outside, put 4i inside put 1 0 8 26i -20



4i)..1....0....8....26i....-20.

.....1...4i...-8....-6i......4



(remember i^2 = -1)





4i because 4i times 1 + 0 = 4i

-8 because 4i times 4i is 16i^2 which is -16, plus 8 = -8

-6i because 4i times -8 is -32i plus 26i = -6i

4 because 4i times -6i is -24i^2 which is 24 minus 20 is 4



So the answer is x^3 + 4ix^2 - 8x - 6i, remainder 4