# How do you plot 6-7i and find its absolute value?

Jul 6, 2017

$| 6 - 7 i | = \sqrt{85} = 9.219 \ldots$

#### Explanation:

Let:

$z = 6 - 7 i$

Then:

$R e \left(z\right) = 6$
$I m \left(z\right) = - 7$

Thus $z$ will be at coordinate $\left(6 , - 7\right)$ on the argand plane.

We calculate the absolute value, or modulus, of the number as follows:

$| z | = | 6 - 7 i |$
$\text{ } = \sqrt{{6}^{2} + {\left(- 7\right)}^{2}}$
$\text{ } = \sqrt{36 + 49}$
$\text{ } = \sqrt{85}$
$\text{ } = 9.219 \ldots$