# How do you find abs( 7-5i )?

##### 2 Answers
Jul 28, 2018

$\sqrt{74}$

#### Explanation:

$\text{given a complex number "z=x+yi" then}$

$\text{it's magnitude is}$

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

$\text{here "x=7" and } y = - 5$

$| 7 - 5 i | = \sqrt{{7}^{2} + {\left(- 5\right)}^{2}} = \sqrt{74}$

$\setminus \sqrt{74}$

#### Explanation:

The absolute value of any complex number $\left(a + i b\right)$ is given as

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

$\setminus \therefore | 7 - 5 i |$

$= \setminus \sqrt{{7}^{2} + {\left(- 5\right)}^{2}}$

$= \setminus \sqrt{74}$