# Complex Conjugate

• Mar 21st 2011, 01:18 PM
AngusBurger
Complex Conjugate
I have seen other threads on this topic, but did not really understand them. They just seemed to sprawl off into nomenclature that I didn't follow, so I probably shouldn't actually be doing this, but hey.

My question is, what is 1/(0.8-j1.6)?

As far as I understood, it may be the same as z/z^2, although that may be only part way to representing it differently.
• Mar 21st 2011, 01:25 PM
TheChaz
How about an example, where I use i instead of j. We have the property that $i^2 = -1$.

For example: $\frac{1}{3 + 4i}$

Now the "complex conjugate" of $3 + 4i$ is $3 - 4i$, so we multiply the numerator and denominator by this to get

$\frac{1}{3 + 4i} \times \frac{3 - 4i}{3 - 4i} = \frac{3 - 4i}{9 - 16i^2}$

And using what we know about i, this equals

$\frac{3 - 4i}{9 + 16} = \frac{3 - 4i}{25} = \frac{3}{25} - \frac{4}{25}i$

Did you mean $\frac{\overline{z}}{z^2}$ ??
• Mar 21st 2011, 01:27 PM
Plato
Quote:

Originally Posted by AngusBurger
As far as I understood, it may be the same as z/z^2, although that may be only part way to representing it differently.

You have incorrect notation: $\dfrac{1}{z}=\dfrac{\overline{\,z\,}}{|z|^2}$
• Mar 21st 2011, 01:33 PM
AngusBurger
Sorry, that is what I meant.

It's not as outrageous as I thought it would be, then. It's just Cartesian division (which is what I used to get the equation in the first place). Thank you for the clarification.