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

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Answer 1 · 2016-05-26T04:11:21

$|-4+2i|=2sqrt5~=4.5$

We have the complex number

$c=-4+2i$

There are two equivalent expressions for the magnitude of an imaginary number, one in terms of the real and imaginary parts and

$|c|=+sqrt{RRe(c)^2 + Im(c)^2}$ ,

and another in terms of the complex conjugate

$=+ sqrt(c*bar{c})$ .

I'm going to use the first expression because it's simpler, in certian cases the 2nd may be more useful.

We need the real part and imaginary parts of $-4+2i$
$RRe(-4+2i)=-4$
$Im(-4+2i)=2$
$|-4+2i|=sqrt{(-4)^2+(2)^2}=sqrt{16+4}=sqrt{20}=2sqrt5~=4.5$

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