How do you find abs( 14i )?

Apr 4, 2016

$| 14 i | = 14$

Explanation:

Given a complex number $a + b i$, the modulus $| a + b i |$ of the complex number is given by

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

In this case, we have

$| 14 i | = | 0 + 14 i | = \sqrt{{0}^{2} + {14}^{2}} = 14$

Note that in general, for any $b \in \mathbb{R}$, we have $| b i | = \sqrt{{b}^{2}} = | b |$

Apr 4, 2016

14

Explanation:

$| a b | = | a | | b |$.
i is unit vector in the direction of the axis of imaginaries. $| i | = 1$.