# How do you find the absolute value of z = 2 - 6i?

Sep 23, 2016

The Ab. Val. $= 2 \sqrt{10} \approx 6.3244$.

#### Explanation:

We denote The Absolute Value of a Complex No. $z = a + i b$ by |z|, &,

it is defined by,

$| z | = | a + i b | = \sqrt{{a}^{2} + {b}^{2}} .$

In our case,

$| z | = | 2 - 6 i | = \sqrt{{2}^{2} + {\left(- 6\right)}^{2}} = \sqrt{40} = 2 \sqrt{10}$.

Taking, #sqrt10~~3.1622,

The Ab. Val. $= 2 \sqrt{10} \approx 6.3244$.