How do you find abs(-5i)?

1 Answer
Jun 6, 2016

Apply the definition $| a + b i | = \sqrt{{a}^{2} + {b}^{2}}$ to find that

$| - 5 i | = 5$

Explanation:

The modulus of a complex number $a + b i$, denoted $| a + b i |$, is given by

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

and is an extension of the absolute value function, which applies to reals. The latter represents the distance from the real number to $0$ on the number line, and the former represents the distance of the complex number to the origin on the complex plane.

Applying this definition to our given complex number, we have:

$| - 5 i | = | 0 + \left(- 5\right) i |$

$= \sqrt{{0}^{2} + {\left(- 5\right)}^{2}}$

$= \sqrt{0 + 25}$

$= \sqrt{25}$

$= 5$