1. ## Diving complex numbers

How would I divide
$\displaystyle 1/ 1+i - 1/1-i$

2. Originally Posted by colerelm1
How would I divide
$\displaystyle 1/ 1+i - 1/1-i$
Do you mean $\displaystyle \dfrac{1}{1+i}-\dfrac{1}{1-i}$?

First combine the two fractions by getting a common denominator: $\displaystyle \dfrac{1}{1+i}-\dfrac{1}{1-i}=\dfrac{(1-i)-(1+i)}{(1+i)(1-i)}=\ldots$.

Can you finish the problem?

3. Well I had actually already gotten that far....I just dont know what I should do right after that step.

4. if you got that far, you should know that it becomes:

$\displaystyle \dfrac{(1-i)-(1+i)}{(1+i)(1-i)}= \dfrac{1-i-1-i}{(1)^{2}-(i)^{2}}$

what is $\displaystyle i^2$?

5. Here is suggestion on a different way to approach this sort of problem.

Recall that $\displaystyle \dfrac{1}{z} = \dfrac{{\overline z }}{{\left| z \right|^2 }}$.

So $\displaystyle \dfrac{1}{{1 + i}} - \dfrac{1}{{1 - i}}$ becomes $\displaystyle \dfrac{{1 - i}}{2} - \dfrac{{1 + i}}{2}$ which is easier to deal with.