# Diamond said that the absolute value of (-3-sqrt5 i) is sqrt34 and De'Andre said it is sqrt14. Who is correct and why?

Jan 21, 2018

De'Andre is correct

#### Explanation:

for any complex number say of the form
$z = x + i y$ the absolute value is given by
${\left({x}^{2} + {y}^{2}\right)}^{\frac{1}{2}}$
hence the absolute value of $- 3 - {\left(5\right)}^{\frac{1}{2}} i$
is given by
${\left({3}^{2} + {5}^{\frac{1}{2} \cdot 2}\right)}^{\frac{1}{2}}$
which is $\sqrt[]{14}$
hope u find it helpful :)