f(x)=x^4-6x^3+11x^2+12x-26 divided by 3-2i
3-2i | 1 -6 11 12 -26
|____________________________
Bring down the 1
3-2i | 1 -6 11 12 -26
|
1
Multiply the 1 by the 3-2i: 1(3-2i) = 3-2i. Write that under the -6
like this:
3-2i | 1 -6 11 12 -26
| 3-2i
1
Add -6 and 3-2i, getting -3-2i. Put that underneath the line to
the right of the 1, like this:
3-2i | 1 -6 11 12 -26
| 3-2i
1 -3-2i
Multiply the -3-2i by the 3-2i: (-3-2i)(3-2i) = -9+6i-6i+4i²
= -9+4(-1) = -9-4 = -13. Write than under the 11 like this:
3-2i | 1 -6 11 12 -26
| 3-2i -13
1 -3-2i
Add 11 and -13, getting -2. Put that underneath the line to
the right of the -3-2i, like this:
3-2i | 1 -6 11 12 -26
| 3-2i -13
1 -3-2i -2
Multiply the -2 by the 3-2i: -2(3-2i) =-6+4i. Write that under the 12
like this:
3-2i | 1 -6 11 12 -26
| 3-2i -13 -6+4i
1 -3-2i -2 6+4i
Multiply the 6+4i by the 3-2i: (6+4i)(3-2i) = 18-12i+12i-8i²
= 18-8(-1) = 18+8 = 26. Write than under the -26 like this:
3-2i | 1 -6 11 12 -26
| 3-2i -13 -6+4i 26
1 -3-2i -2 6+4i
Add and get 0 remainder
3-2i | 1 -6 11 12 -26
| 3-2i -13 -6+4i 26
1 -3-2i -2 6+4i 0
We interpret that bottom line as coefficients of a
polynomial of one less degree than the original. The
degree of the original is 4, so this will be of degree 3:
x³ + (-3-2i)x² - 2x + (6+4i)
That's the answer. or you can factor out a negative
from the second coefficiens:
x³ - (3+2i)x² - 2x + (6+4i)
Edwin
