# divide polynomial with x+i

• May 10th 2008, 07:17 PM
gumi
divide polynomial with x+i
x^50-20x^32-3x+1 divideed by x+i

how do u divide by i? can some eplain please.
• May 10th 2008, 07:43 PM
Reckoner
Quote:

Originally Posted by gumi
x^50-20x^32-3x+1 divideed by x+i

how do u divide by i? can some eplain please.

When dividing by a complex number, multiply the numerator and denominator by its conjugate.

For example:

$\displaystyle \frac{10}{4 + 2\,\text{i}}$

$\displaystyle =\frac{10\color{red}\left(4 - 2\,\text{i}\right)}{\left(4 + 2\,\text{i}\right)\color{red}\left(4 - 2\,\text{i}\right)}$

$\displaystyle =\frac{\color{red}40 - 20\,\text{i}}{\color{red}16 - 4\,\text{i}^2}$

Noting that $\displaystyle \text{i}^2 = -1$, we have

$\displaystyle \frac{40 - 20\,\text{i}}{16 - {\color{red}(-1)}4}$

$\displaystyle =\frac{40 - 20\,\text{i}}{\color{red}20}$

$\displaystyle =\frac{40}{20} - \frac{20\,\text{i}}{20}$

$\displaystyle =2 - \text{i}$

Does that help?
• May 10th 2008, 08:39 PM
gumi
yes it does thanks