# How do you find the absolute value of 4-8i?

Jul 12, 2016

$| 4 - 8 i | = \sqrt{{4}^{2} + {\left(- 8\right)}^{2}} = \sqrt{16 + 64} = \sqrt{80} = 4 \sqrt{5.}$

Taking, $\sqrt{5} \cong 2.236 , | z \lceiling = 4 \times 2.236 = 8.944$

#### Explanation:

Absolute Value or Modulus $| z |$of a Complex No. $z = x + i y$ is defined by,

$| z | = \sqrt{{x}^{2} + {y}^{2}} .$

$| 4 - 8 i | = \sqrt{{4}^{2} + {\left(- 8\right)}^{2}} = \sqrt{16 + 64} = \sqrt{80} = 4 \sqrt{5}$

Taking, $\sqrt{5} \cong 2.236 , | z \lceiling = 4 \times 2.236 = 8.944$