# ap1.3.51 are complex numbers, show that

#### karush

##### Well-known member
$\textsf{ If$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

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#### MarkFL

Staff member
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
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

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