How do you find $| - 2 + 4 i |$ $abs(-2 + 4i )$ ?

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Answer 1 · 2016-03-31T02:41:50

$| - 2 + 4 i | = 2 \sqrt{5}$ $|-2+4i| =2sqrt(5)$

The modulus of a complex number $a + b i$ $a+bi$ is defined as

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

(Note that this is the distance from the origin to the point $(a, b)$ $(a,b)$ on the complex plane)

In this case, that gives us

$| - 2 + 4 i | = \sqrt{{(- 2)}^{2} + 4^{2}}$ $|-2+4i| = sqrt((-2)^2+4^2)$

$= \sqrt{4 + 16}$ $=sqrt(4+16)$

$= \sqrt{20}$ $=sqrt(20)$

$= 2 \sqrt{5}$ $=2sqrt(5)$

How do you find abs(-2 + 4i )|−2+4i|abs(-2 + 4i )?