MHB Ap1.3.51 are complex numbers, show that

[karush]

$\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 systemsso much help is mahalo

View attachment 8565​

 

[MarkFL]

I would begin with:

$$u=x_u+y_ui$$

$$z=x_z+y_zi$$

And the see where the algebra leads. :)

 

[karush]

I would begin with:

$$u=x_u+y_ui$$

$$z=x_z+y_zi$$

And the see where the algebra leads. :)

accually what does the bar over mean

 

[MarkFL]

accually what does the bar over mean

That means "the conjugate of." And so, using my prior definitions:

$$\overline{u}=x_u-y_ui$$

$$\overline{z}=x_z-y_zi$$

 

[Opalg]

$\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 $$\bar{z}u=\overline{z\bar{u}}
\text{ and }
\overline{\left(\frac{z}{u} \right)}=\frac{\bar{z}}{\bar{u}}$$