# How do you find absolute value of 4+2i, 8i, and -3 + 7i?

Apr 15, 2018

$2 \sqrt{5} , 8 \text{ and } \sqrt{58}$

#### Explanation:

$\text{given a complex number } x + y i$

$\text{then the absolute value is}$

•color(white)(x)|x+yi|=sqrt(x^2+y^2)

$4 + 2 i \text{ has "x=4" and } y = 2$

$\Rightarrow | 4 + 2 i | = \sqrt{{4}^{2} + {2}^{2}} = \sqrt{20} = 2 \sqrt{5}$

$8 i \text{ has "x=0" and } y = 8$

$\Rightarrow | 8 i | = \sqrt{{0}^{2} + {8}^{2}} = 8$

$- 3 + 7 i \text{ has "x=-3" and } y = 7$

$\Rightarrow | - 3 + 7 i | = \sqrt{{\left(- 3\right)}^{2} + {7}^{2}} = \sqrt{58}$