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ap1.3.51 are complex numbers, show that

karush

Well-known member
Jan 31, 2012
2,648
$\textsf{ If $z$ and $u$ are complex numbers, show that}$
$$\displaystyle\bar{z}u=\bar{z}\bar{u}
\textit{ and }
\displaystyle \left(\frac{z}{u} \right)=\frac{\bar{z}}{\bar{u}}$$


ok couldn't find good example on what this is
and I'm not good at 2 page proof systems


so much help is mahalo
output-onlinepngtools.png
 
Last edited:

MarkFL

Administrator
Staff member
Feb 24, 2012
13,734
I would begin with:

\(\displaystyle u=x_u+y_ui\)

\(\displaystyle z=x_z+y_zi\)

And the see where the algebra leads. :)
 

karush

Well-known member
Jan 31, 2012
2,648
I would begin with:

\(\displaystyle u=x_u+y_ui\)

\(\displaystyle z=x_z+y_zi\)

And the see where the algebra leads. :)
accually what does the bar over mean
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,734
accually what does the bar over mean
That means "the conjugate of." And so, using my prior definitions:

\(\displaystyle \overline{u}=x_u-y_ui\)

\(\displaystyle \overline{z}=x_z-y_zi\)
 

Opalg

MHB Oldtimer
Staff member
Feb 7, 2012
2,678
$\textsf{ If $z$ and $u$ are complex numbers, show that}$
$$\displaystyle\bar{z}u=\bar{z}\bar{u}
\textit{ and }
\displaystyle \left(\frac{z}{u} \right)=\frac{\bar{z}}{\bar{u}}$$
There are some bars missing. I think that the problem should be asking you to show that $$\bar{z}u=\overline{z\bar{u}}
\text{ and }
\overline{\left(\frac{z}{u} \right)}=\frac{\bar{z}}{\bar{u}}$$