# complex conjugate

• Oct 25th 2009, 08:31 AM
alexandrabel90
complex conjugate
can i ask if Z= r ( cos X + i sin X), then Z* = r ( cos X - i sin X) or Z* = (1/r) ( cos X - i sin X)

thanks!
• Oct 25th 2009, 09:31 AM
utopiaNow
Quote:

Originally Posted by alexandrabel90
can i ask if Z= r ( cos X + i sin X), then Z* = r ( cos X - i sin X) or Z* = (1/r) ( cos X - i sin X)

thanks!

I'm assuming you're asking what the complex conjugate of $\displaystyle z = r(\cos{X} + i\sin{X})$ is? If, so then just remember if $\displaystyle z = a + ib$, where $\displaystyle a, b \in \mathbb{R}$, then the complex conjugate is simply $\displaystyle \bar{z} = a - ib$. So if we have $\displaystyle z = r(\cos{X} + i\sin{X})$, then if we re-arrange to get it to the form $\displaystyle z = a + ib$, we see we get $\displaystyle z = r\cos{X} + ri\sin{X}$. Therefore $\displaystyle \bar{z}$ or $\displaystyle z^* = r\cos{X} - ri\sin{X} = r ( \cos{X} - i \sin{X})$ is the complex conjugate.

So to sum up complex conjugate of Z= r ( cos X + i sin X) is Z* = r ( cos X - i sin X).